Method and device for superresolution optical measurement using singular optics

ABSTRACT

An optical method of measurement and an optical apparatus for determining the spatial position of at least one luminous object on a sample. A sequence of at least two compact luminous distributions of different topological families is projected onto the sample, and light re-emitted by the at least one luminous object is detected. At least one optical image is generated for each luminous distribution on the basis of the light detected. The optical images are analyzed to obtain spatiotemporal information regarding the light re-emitted by the at least one luminous object, or location of the at least one luminous object.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of pending U.S. patentapplication Ser. No. 17/087,238, scheduled to issue as U.S. Pat. No.11,236,992, which is a continuation of U.S. patent application Ser. No.16/557,030, now issued as U.S. Pat. No. 10,823,551, which is acontinuation of U.S. patent application Ser. No. 15/812,016, now issuedas U.S. Pat. No. 10,401,153, which is a continuation of U.S. patentapplication Ser. No. 14/998,051, now issued as U.S. Pat. No. 9,846,030,itself a continuation of U.S. Ser. No. 13/822,355 (issued Feb. 2, 2016as U.S. Pat. No. 9,250,185), which was a US national phase entry ofPCT/FR2011/000555, filed Oct. 14, 2011, through which it claimed thebenefit of French application no. FR1004067, filed Oct. 15, 2010. Theentire contents of each of the foregoing applications are incorporatedby reference herein.

BACKGROUND

The present invention relates to a method and an optical measuringdevice. It finds applications in particular in microscopy, for examplein the field of biology and the acquisition of biological informationfrom optical observation.

A microscope is an optical instrument generally used to view, analyze ormeasure objects too small for the naked eye.

We use the term biological to describe any biological entity in lifesciences, regardless of its origin, human, animal or vegetal and of thepurpose of the observation, be it for research, diagnostic ortherapeutic application. This term includes the medical uses of themethod described. Microscopy is used in the field of biology, forexample, to observe, study and measure biological entities (objects) andtheir dynamics.

The usual definitions are used for: optical diffraction limit, Rayleighcriterion, Airy disk and its radius and diameter. We use in the contextof the invention, the terms of superresolution, superresolved,superresolution imaging and superresolution microscopy to describeoptical data acquisition, optical imaging and microscopy at a resolutionhigher than the optical diffraction limit. The usual definitions areused for fluorescence and for fluorophores.

Referring now to FIG. 1 , which shows an illustration of the paradigm ofMicroscopy, 100, in the field of Biology.

Microscopy comprises the illumination, by a light source, not shown,using a microscope, 10, of a biological sample, 11, and thetime-dependent measurement, using either visual observation or adetection module 12, of the light emitted by the sample.

The sample in Biology comprises a single—or a plurality—of differentbiological entities, 13 and 14, positioned at different positions.

Examples of such objects are, among others, a cell, a virus, a proteinand a DNA fragment.

Fluorescence microscopy is one of the variants of microscopy, it hasreplaced in many biological applications, the other microscopytechniques.

A fluorescence microscope is an optical microscope used to studyproperties of organic or inorganic substances using the phenomena offluorescence instead of, or in addition to other modalities such asreflection and absorption.

We refer again to FIG. 1 , describing a fluorescence microscope; influorescence microscopy fluorophores, tiny point sources, 15 to 18,based on the physical phenomenon of one photon fluorescence, are fixedat specific positions of predetermined biological objects, 13 and 14;the light emitted by the fluorophores is observed instead of observingthe light emitted by the biological objects, 13 and 14, themselves.

The sample is illuminated by light of wavelength, or specificwavelengths, which is absorbed by the fluorophore, thereby inducing theemission of light at different, higher, wavelengths.

The illumination light is separated from the emitted fluorescence, whichis lower, by the use of a spectral emission filter.

Fluorophores have become an important tool for the visualization ofbiological objects. The activity and the biological informationincluding details above the limit of resolution of 200 nm aresystematically viewed and measured using fluorescence microscopy. Thisresolution limit is derived from the Rayleigh criterion, which in thebest case, reaches 200 nm in systems designed specifically. For a longtime, until the emergence of superresolution techniques described below,it was assumed that optical techniques, including fluorescencemicroscopy, are unable to visualize details smaller than the Rayleighcriterion, which is about 200 nm.

However, other fundamental biological activities also occur at scalessmaller than 200 nm in biological samples. At this level of spatialresolution, important phenomena can be observed: the biologicalprocesses at the scale of intracellular, cell information transfer, thefolding and unfolding of the proteins and changes in the DNA and RNA.For example, the measurement of this intracellular information open newavenues for understanding the biological activity, and lead to progressin understanding and monitoring of research and medical diagnostics.

The main implementations of fluorescence microscopy, as described indetail in the literature, are the confocal microscope, often used in ascanning configuration or spinning disc microscope, and the wide-fieldimaging microscope.

Referring now to FIG. 2 which is a simplified representation of aconfocal fluorescence microscope of the prior art 200.

A confocal fluorescence microscope, FIG. 2 is an optical instrument. Itsmain hardware components are shown in FIG. 2 . They include:

a light source, 20,

an optomechanical frame not shown,

a cube filter, 21,

a microscope objective 22,

a detector assembly, 23, and

a processing unit, not shown.

The light source 20, which may be an arc lamp or a laser, creates lightenergy necessary for fluorescence.

The Optomechanical frame, not shown, is the support of all the opticalcomponents and auxiliary optics and includes alignment capacities.

It also includes optical elements, not shown, capable of shaping thebeam to allow its focus point of a minimum size by means of themicroscope objective.

It can also comprise, in a confocal scanning fluorescence, a spatial orangular scanning mechanism, not shown, to change the position of thepoint source with respect to the object to be measured.

The scanning mechanism can alternatively

-   -   mechanically translate the object, for example by using a        translation plate,    -   optically scan the beam on the object, for example using a set        of galvanometric mirrors or acousto-optical translators, or    -   use any combination of these translation means, mechanical or        optical.

In a confocal scanning fluorescence, the information is collected pointby point, using the scanning mechanism.

It can also comprise, in a rotating disk type confocal fluorescence, arotating disc having a plurality of pinholes, allowing the simultaneousprojection of a plurality of points. In a confocal fluorescence rotatingdisk, a set of points, corresponding to the pinhole is acquired at anytime and the rotation of the disk allows to scan the entire surface ofthe sample for a given longitudinal position.

The cube of filters, 21, channels the different optical signals andavoids contamination of the fluorescence signal by the emission. Thecube is composed of filters: excitation filter, 210 dichroic mirror,211, and emission filter 212. The filters and the dichroic mirror areselected according to the wavelength of excitation and emission spectralcharacteristics of the fluorophore.

The microscope objective 22 focuses the light created by the source inthe focal plane of the lens 24, a light distribution pattern of smallsize, the optimum light distribution consisting of the Airy disk. Themicroscope objective 22, also collects back fluorescent light emitted bythe fluorophores.

For a confocal scanning fluorescence the system can be descanned, thatis to say, the return light can pass through the scanning mechanism tocompensate for the translation due to scanning.

A detector lens, 25, creates, in the image plane of the detector 26, amagnified image of the focal plane of the lens 24.

A confocal hole, 28, is theoretically placed in the image plane of thedetector 26. In most practical systems, the confocal hole, 28, is placedin an intermediate imaging plane, not shown, and reimaged onto the imageplane of the detector 26.

The assembly of the detector, 23, detects the fluorescent intensity inthe overall illuminated volume, and converts it into digital signal. Fora confocal scanning microscope, the detector assembly comprises adetector of a single element, such as a PMT or SPAD. For a confocalmicroscope using a rotary disc, the detector assembly is comprised of amatrix of detector elements, such as a CCD, a EMCCD, a CMOS or a matrixof SPAD.

All components mounted from the light source to the dichroic filter isthe illumination path, 201. The detection channel, 202, represents allthe components mounted from the dichroic filter to the assembly of thedetector.

The elementary optical process of a confocal microscope can be segmentedinto six steps:

Projecting light on the volume analyzed

-   -   Fluorescent light emission by fluorophores    -   Imaging of the fluorophores in the focal plane    -   Limitation in the focal plane of light analyzed by confocal hole    -   Integration of light analyzed by a photoelectric detector

Display of the measured intensity as a pixel value in an image

Fluorescence microscopes are available from several manufacturers, suchas Nikon, Zeiss, Leica and Olympus. Fluorescence microscopes can beeither standard microscopes suitable for fluorescence or microscopesoptimized specifically for fluorescence. Modern microscopes areversatile instruments capable of operating in many different modalities,including, but not limited to, fluorescence modalities, using the sameplatform and most optomechanical components. Most fluorescencemicroscopes are developed as an open platform, capable of performingseveral additional features with minimal modifications. Otherfluorescence microscopes are instruments dedicated, adapted for aspecific task, such as medical diagnosis or pharmaceuticals.

New optical methods, methods for superresolution are capable ofdiscriminating fluorophores, below the Rayleigh criterion. These methodsare being developed by several companies, laboratories and researchersand some of the instruments using these methods, the superresolutionmicroscopes, are commercially available. Several comparative analysis ofsuperresolution methods have recently been published in the literature,as the article written by Ricardo Henriques and Mr Musa Mhlanga,entitled “PALM and STORM: What hides beyond the Rayleigh limit?”, orArticle written by Kelly Rae Chi called “Super resolution microscopy:breaking the limits.”

New optical methods, methods for superresolution are capable ofdiscriminating fluorophores, below the Rayleigh criterion. These methodsare being developed by several companies, laboratories and researchersand some of the instruments using these methods, the superresolutionmicroscopes, are commercially available. Several comparative analysis ofsuperresolution methods have recently been published in the literature,such as the article written by Ricardo Henriques and Mr. Musa Mhlanga(“PALM and STORM: What hides beyond the Rayleigh limit?”, BiotechnologyJournal, 4, 846-857 (2009)), or the article written by Kelly Rae Chi(“Super resolution microscopy: breaking the limits”, Nature Methods, 6,15-18 (2008)).

An updated bibliography on the superresolution is on the website of thecompany Zeiss Co. (“Zeiss Microscopy and image analysis”, (2011),retrieved at http://www.zeiss.eom/4125681C00466C26/7Qpen) and on thewebsite of the company Nikon Co. (“MicroscopyU: the source forMicroscopy Education” (2011) retrieved at http://www.microscopvu.com/)(hereinafter, “Nikon (2011)”.

New superresolution techniques allow to obtain information beyond theresolution limit. The main problem of all existing superresolutiontechniques is that the envelope of performance, expressed in terms oflateral resolution of longitudinal resolution, speed, light intensitynecessary for phototoxicity in the biological object, of ability tomeasure different objects, is very limited.

In addition, most of the methods and instruments can providesuperresolution either a good lateral resolution or a good longitudinalresolution, but rarely both.

In addition, all these instruments are complex and require a highlyskilled operator.

In addition, these instruments can generally observe a small part ofbiological specimens due to strong operational limitations, such as, forsome of them, a shallow depth of field or a requirement of very highlight intensities, harmful to cells.

Another problem with the methods and instruments of super resolution, isthat most of them are able to recover in the illuminated volume, theattributes of a single fluorophore, but fail to recognize the presenceof simultaneously several fluorophores and measuring their attributes.

An additional problem with the methods and instruments ofsuperresolution is that these methods and instruments are presented tousers and perceived by them as a general tool, able to replace thestandard or confocal microscopes. However, the methods and instrumentssuperresolution lack the simplicity, robustness, ease of use andcompetitive prices of standard microscopes which hinders their use asresearch tools or as general diagnostic tools.

Another problem with existing superresolution methods and tools is thatmost of these methods and tools are designed as stand-alone instrumentsdesigned to replace standard microscopes. Such an approach requires thereplacement of existing instruments and the renewal of all systems anddevices all the knowledge and know-how related to microscopy platformsand developed over many years.

Another problem with most methods and instruments fluorescencemicroscopy and superresolution is that these methods and tools aredesigned on a paradigm of image acquisition, the entity for which basicinformation is—or more images, or—or more—ROI regions—Region Of Interestbi- or three-dimensional. Algorithmic, systemic and superresolutionmethods described later in the context of the invention will, by theirinherent flexibility, the development of new strategies of acquisition.These acquisition procedures, dynamic and selective, will be defined byan optimized sequence acquisition and interactive and deferredprocessing. They allow a more sophisticated optimization of the usefulinformation, as defined by criteria based on the shape, geometry anddynamics of one or more fluorescent objects, separately or relative oneto the other.

So there is still an urgent need to provide superresolution methods andtools and algorithms methods capable of measuring with high accuracy theattributes of a fluorophore. It is also necessary to provide methods andtools to detect and quantify the presence of multiple fluorophoresplaced in the same volume illuminated.

SUMMARY

A goal of at least one embodiment of the present invention is to providea technique for superresolution fluorescence microscopy in Biology andmore generally to life sciences, and additionally to pharmacology,medicine and diagnostics, that will overcome the shortcomings of theprior art devices.

One of the goals of at least one embodiment of the present invention isto provide a technique for superresolution fluorescence microscopy inbiology to achieve an optical system that is capable of measuring withhigh accuracy the attributes of a fluorophore and recognizing andmeasuring the attributes of multiple fluorophores located in the sameilluminated volume.

Another goal of at least one embodiment of the invention is to provide atechnique for superresolution fluorescence microscopy in biology tomeasure with high precision the attributes of a fluorophore.

Another goal of at least one embodiment of the invention is to provide atechnique for superresolution fluorescence microscopy in biology thatacquires and measure with great precision, the attributes of multiplefluorophores present in the same illuminated volume.

To this end, a first aspect of the invention provides a method ofoptical measurement to determine the spatial position of at least onelight nanoemitter on a sample, the method comprising:

-   -   projecting a sequence of at least two light distributions of        different topological families on the sample,    -   detecting of the light reemitted by said at least one light        nanoemitter from the sample;    -   generating at least one optical image for each light        distribution, from the detected light, and    -   analyzing algorithmically the optical images to obtain a        location information of said at least one light nanoemitter.

The detection may comprise the detection of the reflected light at amean wavelength λ. The reflected light can be collected by a highnumerical aperture objective. Both distributions can be compact.

The plurality of distributions may be generated sequentially in time, orcreated simultaneously.

According to an embodiment the two compact light distributions arecollocated on the sample.

According to one embodiment said at least two compact lightdistributions of different topological families are created byinterference between a regular wave and a singular wave, or between twosingular waves, and spatial differentiation between said at least twodistributions is created by varying at least one of the followingparameters:

-   -   a) at least one of the parameters of the regular wave;    -   b) at least one parameter of at least one singular wave and    -   c) a phase difference between the regular wave and the singular        wave or between two singular waves.

The various parameters may include amplitude, phase, polarization,coherence, for example.

According to one embodiment of the process included the creation from anincident light wave, two light collocated waves one regular and onesingular.

According to one embodiment the method further includes the separationof an incident regular wave, into two regular waves following separategeometric paths; transforming, at least one of the regular optical wavesin a singular optical wave and fusion of the two created emergingoptical waves.

According to one embodiment the method further includes at least one ofthe following steps:

-   -   control of the relative amplitude of the regular—and/or singular        waves;    -   control, following a predetermined sequence, of the polarization        and/or the phase state of the input or output light wave from a        crystalline sub-module creating regular and singular waves; the        control of the shape of singular or regular waves, and    -   aligning the central position of the light distribution of a        wave in relation to the other.

According to one embodiment, the process further included formatting,statically or dynamically, the emerging polarization of the saidsuperimposed light distributions, able to mitigate vector effects, onthe shape and size of said compact light distributions, effects createdby a high numerical aperture lens used for generating optical images, byshaping the emerging polarization by providing a static, rotationallysymmetrical, polarization state such that a circular polarization,radial or azimuthal and/or a dynamic polarization state.

According to one embodiment said at least two light distributions arecreated by controlling the intensity of the different modes of amultimode laser.

According to one embodiment, a region of a size substantially less thana mean wavelength λ of the reflected light exists in the sample, whereinthe value of a specific mathematical combination of the intensities ofsaid at least compact two light distributions of different topologicalfamilies is positive for lateral positions of said light distributionportion included in said region, and wherein said specific combinationmathematical approaches zero in all other parts of the lightdistribution beyond said region.

According to one embodiment at least one nanoemitter is a fluorophorewith a sequence of fluorescence light intensities which depends of theincident intensity of the sequence of compact light distributions ofdifferent topological families on said fluorophore thus characterizingthe spatial position of said fluorophore.

According to another embodiment at least two of the nanoemitters arefluorophores, located at different spatial positions, each fluorophoreemitting light with an intensity depending on the incident intensity ofthe sequence of compact light distributions of different topologicalfamilies on the said at least two fluorophores thereby characterizingthe spatial position of at least two fluorophores.

According to one embodiment a region whose size is substantially smallerthan the wavelength λ of the reflected light, exists on the sample,wherein a comparison of a plurality of mathematical combinations of thesaid sequence of compact light distributions of different topologicalfamilies, can differentiate between at least one of the following:

-   -   a) a single light nanoemitter;    -   b) a plurality of collocated light nanoemitters, and    -   c) a plurality of light nanoemitters located at a distance from        each other, thereby determining the distance between the light        nanoemitters.

According to one embodiment the method further comprises varying thesequence of said at least two light distributions and/or the position ofthe sequence of said at least two light distributions as a function ofmeasured data or external information.

According to one embodiment, the projection of light distributions ofdifferent topologies is created by the conical diffraction and modifiedby a variation of the polarization states of input and output of atleast one crystal creating the conical diffraction effect.

According to one embodiment, the spatial position of at least onemeasured light nanoemitter is the lateral position of said at least onelight nanoemitter.

A second aspect of the invention provides a method of opticalmeasurement to determine the spatial position of a plurality of lightpoint-sources the method comprising detecting light emitted by theplurality of light point-sources; and the separation of the lightemitted on a plurality of sensors for simultaneous or sequentialdetection; and the proportion of the light emitted by a lightpoint-source, channeled to a specific detector, being dependent on thespatial position of said light point-source; and the generation of theoptical images from the detected light; and the algorithmic analysis ofoptical images to obtain a location information of the plurality oflight point-sources.

According to one embodiment, each light point-source corresponds to oneor more of the several nanoemitters and the method includes apreliminary step comprising the illumination by incident light of thenanoemitters of the sample for detecting the light remitted bynanoemitters for locating the nanoemitters.

According to an embodiment the spatial position measured is thelongitudinal position of each light point-source or light nanoemitter.

According to one embodiment, the emitted light is separated according tothe longitudinal position of each light point-source or nanoemitter oraccording to the wavelength emitted by each light point-source ornanoemitter.

According to an embodiment the separation of the emitted light isperformed so as to separate, to a plurality of detection channels, thecollimated emitted light, emerging from the light sources positioned atthe focal plane of the lens, from the non-collimated emitted lightemerging from point-sources lying above or beyond the focal plane.

According to one embodiment the method further comprises the parametervariation of the detection channels based on measured data or externalinformation.

According to one embodiment the method further comprises at least one ofthe following steps:

-   -   generating, from each light point-source, a beam of quasi        parallel light, the light beam differing from the parallel light        by an angle of convergence or divergence, the value of the angle        being a function of the longitudinal position of each light        point-source;    -   generating, from an incident light wave, two collocated light        waves, of orthogonal polarizations and different geometries, one        regular and one singular, the ratio of energy between the        regular and singular waves being a function of the angle of        convergence or divergence of the light beam and through it of        the longitudinal position of the point source, the change of        polarization or geometry suitable for separating waves regular        and singular based on a polarization state thereof, or a        geometric shape thereof.

According to one embodiment the method further comprises the separationof the light intensities of the plurality of re-emitted light sourcesinto a plurality of independent channels with orthogonal polarizations,by using a polarization beam splitter, and merging the light intensitiesemerging from each channel, so that the length of the longitudinalposition of the polarization or the pipe geometry of the light intensityin the light is maintained by the merger.

According to one embodiment the method further comprises focusing thelight point sources positioned at a given longitudinal position, and thedefocusing of the light sources positioned before and after saidlongitudinal position, the light distribution different from the focusin dependence on the longitudinal position of each point source.

According to one embodiment the method further comprises generating,from the incident light wave, two light waves of differentpolarizations, the ratio of energy between the waves of differentpolarizations being a function of the spatial distribution at the pointof focusing and through it of the longitudinal position of the lightpoint-source, and the separation of the regular and singular waves onthe basis of its state of polarization or of its geometric shape.

According to one embodiment the detection of the light emitted orre-emitted is limited in the focal plane of the microscope objective.according to one embodiment, said at least optical image is generated byusing the optical microscope, as for example a confocal microscope

A third aspect of the invention provides an optical measuring device fordetermining the spatial position of at least one light nanoemitterpositioned on a sample, the device comprising:

-   -   projection means adapted to project a sequence of at least two        compact light distribution different topological families on the        sample;    -   detecting means adapted to detect the reflected light by said at        least one nanoemitter light of the sample,    -   generating means adapted to generate at least one image for each        optical light distribution, from the detected light, and    -   analysis means capable of performing a computational analysis of        the optical images to obtain a location information of said at        least one light nanoemitter.

According to an embodiment of the means of projections are configured tocolocate both compact light distributions on the sample.

According to one embodiment, the projecting means is adapted to createsaid at least two light distributions by interference between a regularwave and a singular wave or between two singular waves, and to create aspatial differentiation between said at least two distributions byvarying at least one of the following parameters:

-   -   a) at least one of the parameters of the regular wave;    -   b) at least one parameter of at least one singular wave and    -   c) a phase difference between the regular wave and the singular        wave or between two singular waves.

According to one embodiment, the device comprises a crystallinesub-module to create from an incident light wave, two collocated lightwaves one regular and one singular said sub-module lens comprising athin biaxial crystal and/or a uniaxial crystal.

According to one embodiment the device comprises an optical sub-moduleadapted to separate a regular incident wave, in two regular waves alongseparate geometric paths, the sub module being configured to transformat least one of the regular optical waves in an singular optical wave,using processing means comprising at least: a subwavelength grating, thegrating step being smaller than the mean wavelength of the reflectedlight, and a thin biaxial or uniaxial crystal, and wherein the opticalmodule is designed as to combine the two created emerging optical waves.

According to one embodiment the device comprises a polarizer partadapted to control the relative amplitude of regular and singular wavesand optionally translating the central position of the lightdistribution of a wave in relation to the other.

According to one embodiment the device comprises an optical controlsub-module of amplitude polarization or phase, comprising at least onecontrollable or adjustable optical element capable of controlling, in apredetermined sequence, the state of polarization and/or phase of thelight input or output wave of the sub-module lens.

According to one embodiment the device comprises a control sub-module,consisting of at least one adjustable optical element capable ofcontrolling the shape of regular or singular waves.

According to one embodiment, the device comprises a polarizationanalyzer and/or a, static or dynamic, sub-module shaping the emergingpolarization of said light distributions, able to mitigate the vectoreffects on the shape and size of each compact light distribution,effects created by a high numerical aperture of the lens used forgenerating optical images, shaping the emerging polarization byproviding a static polarization state, rotationally symmetrical, suchthat the circular, radial or azimuthal polarizations and/or a dynamicstate of polarization.

In another embodiment, the device comprises a multimode laser, in whichthe intensity of the laser modes are controllable and at least twocompact light distributions of different topological families arecreated by controlling the intensity of the different modes of laser.

According to one embodiment, a region of a size substantially smallerthan the mean wavelength λ of the reflected light exists in the sample,wherein the value of a specific mathematical combination of theintensities of at least two compact light distributions of differenttopological families created by the illumination means is positive forlateral positions included in said region, and wherein said specificcombination mathematical approaches zero in all other parts of the lightdistribution beyond said region.

According to one embodiment at least one is a nanoemitter is afluorophore with a sequence of fluorescence light intensities whichdepends on the sequence of incident compact light distributions ofdifferent topological families on said fluorophore thus characterizingthe spatial position of said fluorophore.

According to one embodiment at least two of the nanoemitters arefluorophores, located at different spatial positions, each one of thefluorophore with a sequence of light fluorescence intensities whichdepends on the sequence of incident compact light distributions ofdifferent topological families on the at least two fluorophores therebycharacterizing the spatial position of the at least two fluorophores.

According to one embodiment a region whose size is substantially smallerthan the wavelength λ of the emitted light, exists in the sample, andfurther comprising a comparator for comparing a plurality ofmathematical combinations of said sequence of compact lightdistributions of different topological families, for differentiatingbetween at least one of the following:

-   -   a) a single light nanoemitter,    -   b) a plurality of collocated light nanoemitters, and    -   c) a plurality of nano-tagging light-located at a distance from        each other, thereby determining the distance between the        nano-tagging light.

According to one embodiment, the projecting means is configured to varythe sequence of said at least two light distribution and/or the positionof the sequence of said at least two light distributions as a functionof measured data or external information.

According to one embodiment, the projecting means comprises at least oneconical crystal to perform conical diffraction, and means for varyingthe polarization states of input and output of said at least one conicalcrystal.

According to an embodiment configured to measure the lateral position ofsaid at least one light nanoemitter.

According to a fourth aspect, the invention provides an opticalmeasuring device for determining the spatial position of a plurality oflight point-sources, the device comprising:

-   -   detecting means adapted to detect the light emitted by the        plurality of light point-sources, and    -   separation means adapted to separate the reflected light on a        plurality of sensors for simultaneous or sequential detection        and the proportion of the reemitted light by a light        nanoemitter, channeled to a specific detector, being dependent        on the spatial position of said light nanoemitter, and    -   means for generating image suitable for generating optical        images from the detected light, and    -   analysis means capable of performing a computational analysis of        the optical images to obtain a location information of the        plurality of light point-sources of light.

According to one embodiment the device is configured to measure thelongitudinal position of each light point-source.

According to one embodiment a point-source comprises one or morenanoemitters of the sample and the device comprises illumination meansadapted to illuminate the nanoemitters of the sample by incident light,and detecting means adapted to detect the light remitted by nanoemittersfor locating the nanoemitters.

For example, a fluorophore can be a nanoemitter.

In one embodiment the separating means are configured to separate thereflected light as a function of the longitudinal position of each lightpoint-source or as a function of the wavelength emitted by each lightpoint-source.

In one embodiment the separating means are configured for separatinginto a plurality of detection channels, the reflected light collimatedemerging from the light point-sources, positioned at the focal plane ofthe lens, from the remitted non-collimated light emerging from the lightpoint-sources located before or beyond the focal plane.

According to one embodiment the device further comprises variation meansto vary the parameters of the detection channels based on measured dataor on external information.

According to one embodiment the device further comprises channelingmeans able to channel the light intensities from the plurality of pointsources of light emitted, placed in a small light volume on separatedetectors, and/or at separate geometric positions on the same detector,depending on the longitudinal position of each point source.

According to one embodiment the device further comprises a sub-modulethat interfaces to a microscope objective and to a sub-detection unitand one to the other by auxiliary optics.

According to one embodiment the device comprises optical means adaptedto create, from each point source of the light emitted, a beam of quasiparallel light, the light beam differing from the parallel light by anangle of convergence or divergence, and the value of the angle being afunction of the longitudinal position of each light point-source.

According to one embodiment the device comprises a crystallinesub-module, or a cascade of crystalline sub-modules, eachsub-crystalline module consisting of a biaxial crystal and/or a uniaxialcrystal, and auxiliary optics, the aforesaid sub-crystalline modulebeing adapted to create from the incident collocated light wave twolight waves of orthogonal polarizations and different geometries, oneregular and one singular, the ratio of energy between the regular andsingular waves being function of the angle of convergence or divergenceof the beam and through him the longitudinal position of the pointsource emitter.

According to one embodiment the device comprises means for changing thepolarization or geometry suitable for separating the regular andsingular waves based on a polarization state thereof, or a geometricshape thereof.

According to one embodiment, the device includes

-   -   a beam splitter for separating the polarization of light        intensities of a plurality of point sources of the emitted        light, being part of a longitudinal module of superresolution        allowing [lisibility correction] to separate into two        independent channels with orthogonal polarizations, and    -   means for merging the intensities emerging from each channel of        the longitudinal module of superresolution, so that the        dependence of the longitudinal position of the light intensity        of the polarization or the geometry channels is maintained by        the merger.

According to one embodiment the device comprises optical means able tofocus light point sources of remitted light, positioned at a givenlongitudinal position, and, to slightly defocus the light sources of thereemitted light, positioned before and after said longitudinal position,the light distribution differing from the focusing in dependence of thelongitudinal position of each point source.

According to one embodiment the device comprises means for spatiallyvarying polarization and having at least a uniaxial crystal of variablethickness, a subwavelength grating with step below the mean wavelengthof the reflected light and/or a phase waveplate, creating from theincident light wave two light waves of different polarizations, theratio between the energy of the waves of different polarizations being afunction of the spatial distribution at the focusing point and throughit of the longitudinal position of the point source emitter.

According to one embodiment, the device comprises polarization orgeometry means capable of separating the regular and singular waves onthe basis of their polarization states or on their geometric shapes.

In a fifth aspect, the invention provides an optical measurement todetermine the spatial position of at least one light nanoemitter on asample comprising a microscope, for example, a confocal microscope, ameasuring device according to one embodiment of the third aspect of theinvention, and/or a measuring device according to one embodiment of thefourth aspect of the invention.

According to a sixth aspect, the invention provides a method of opticalmeasurement to determine the spatial position of at least one lightnanoemitter on a sample comprising a measuring method according to anembodiment of the first aspect of the invention to determine the lateralposition of at least one nanoemitter in a sample, and a measuring methodaccording to an embodiment of the second aspect of the invention fordetermining the position of at least one longitudinal nanoemitter on asample.

In another aspect, the invention provides a method of opticalmeasurement consisting of a sequential projection of at least twocompact light distributions of topological families on a sample.

In another aspect, the invention provides an apparatus for performingoptical measurements with a projector for sequential projecting at leasttwo compact light distributions of different topological families on asample.

In another aspect, the invention provides an optical system configuredto create in sequence, on a sample, at least two light distributionsspatially separated from each other, each of said distributions having adiameter less than 1, 5 time the mean wavelength of the reemitted lightfrom the sample, such as combinations of intensities of saiddistributions creating localized characteristics of a size less than 0.5said mean wavelength.

In another aspect, the invention provides an optical system including anoptical apparatus and a illuminated measurement region, the opticalapparatus being configured to sequentially create at least two lightdistribution spatially separated from each other, and defining a set ofpoints in the measurement region comprising all the points of zerointensity one one or another of the distributions, a point located inthe region close to a measurement point of said assembly being less thanor equal to 0, 5 of the radius of the measuring region.

In another aspect, the invention provides an optical system comprisingan optical device and a measurement region to be illuminated, theoptical device being configured to sequentially create at least twolight distributions spatially differentiated from each other anddefining a set of points in the illuminated measurement region,comprising all points of zero intensity and local intensity maximum inone or other of the distributions, a point located near a point of saidassembly being less than or equal to ⅙ of the diameter of the measuringregion.

In another aspect, the invention provides an optical apparatus, and acompact measuring region having a line passing through the center of themeasurement region, the optical apparatus being configured to create alight distribution spatially differentiated, the ratio energy betweenthe intensity along the line passing through a maximum, a minimum andanother maximum.

In another aspect, the invention provides a lateral superresolutionmodule comprising an optical device adapted to sequentially create atleast two light spots spatially differentiated with a diameter less than15 times the emitted average wavelength λ, such as combinations of theintensities of said spots create localized details of a size less than40% of the wavelength λ

An object of at least one embodiment is to provide a new device, amodule for lateral superresolution, comprising an optical device adaptedto create at least two light spots spatially differentiated from adiameter less than 1, 5 times the wavelength, λ, such as localizedfeatures of combinations of the intensity of said spots are smaller than40% of the wavelength λ

Another goal is to provide a vision system, referenced as a modulesuperresolution longitudinal configured to change at least one ofgeometry, geometry and polarization or the polarization of a light beamemerging from a point source depending on the longitudinal position of apoint source.

Another object of at least one embodiment is to provide asuperresolution system for fluorescence microscopy comprising thelateral superresolution module incorporated in the illumination path ofthe microscope, projecting on a sample consisting of a plurality offluorophores, positioned at different lateral positions in the compactlight distribution, a sequence of light spots, of spatiallydifferentiated size of the order of a half wavelength, each of thefluorophores fluorescing with a sequence of fluorescent lightintensities depending linearly or non-linearly of the light incident onthe fluorophore and characterizing a lateral position of thefluorophore.

Another object of at least one embodiment is to provide asuperresolution system for fluorescence microscopy comprising thelongitudinal superresolution module incorporated in the detection pathof the microscope, wherein the light intensity emerging from a pluralityof point sources, placed in a small illuminated volume, are separatedeither on separate detectors or either on distinct geometric positionson the same detector or on a combination of both.

Another object of at least one embodiment is to provide asuperresolution system for fluorescence microscopy, the systemcomprising either a lateral superresolution module incorporated in theillumination path of the microscope, and/or a longitudinalsuperresolution module incorporated in the detection path of themicroscope in a detection circuit for said superresolution fluorescencemicroscope.

Some embodiments of the present invention provide a new technique basedon two optical superresolution modules, new and complementary,referenced herein as the lateral module of superresolution and. Thelateral module of superresolution provides mainly additional lateralresolution and the longitudinal module of superresolution moduleprovides mainly additional longitudinal resolution. Embodiments using asingle module can also be implemented. Both optical modules arecomplemented by suitable algorithms and an improved detection module.The modules can be integrated into existing fluorescent microscopes.Alternatively, fluorescence microscopes dedicated and optimized can bedeveloped around the three dimensional superresolution system.

The methods and devices for superresolution, according to embodiments ofthe present invention differs significantly from conventional techniquesand designs of the prior art, and in so doing, provide a devicedeveloped in order to achieve the techniques and devices of asuperresolution system capable of measuring with high accuracy thedescriptors of a fluorophore and recognize and measure the descriptorsof several fluorophores placed in the same illuminated volume.

The present invention will be better understood from the followingdetailed description of preferred embodiments thereof, taken togetherwith the drawings.

Other objects and advantages of the invention will become apparent tothe reader, and it is considered that these objects and advantages arepart of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described in connection with certain preferredembodiments with reference to the following illustrative figures so thatit can be better understood.

With specific reference now to the figures in detail, it is emphasizedthat the indications represented are presented as an example and forpurposes of illustrative discussion of the preferred embodiments of theinvention and are presented only in order to provide what is consideredto be the description of the most useful and easy to understandprinciples and conceptual aspects of the invention.

In this regard, no attempt is made to show structural details of theinvention in more detail than is necessary for a fundamentalunderstanding of the invention, the description taken with the drawingsmaking apparent to those skilled in the art how the several forms of theinvention may be embodied in practice.

In the drawings:

FIG. 1 is a simplified perspective view of a confocal fluorescencemicroscope of the prior art;

FIG. 2 is a pictorial representation of a simplified superresolutionfluorescence microscopy, in accordance with an embodiment of the presentinvention;

FIG. 3 is a simplified schematic illustration of a setup of a conicaldiffraction module in accordance with one embodiment of the presentinvention;

FIGS. 4 a-4 d are simplified pictorial representations of the twomeasurement paradigms using confocal microscopy and methodology;

FIG. 5 is a simplified pictorial representation of the preferredimplementation of the method of measurement, microscopy platform SRCDP

FIG. 6 is a simplified schematic illustration of a module lateralsuperresolution in accordance with an embodiment of the presentinvention;

FIGS. 7 a-7 b shows tables of light distributions of a conicaldiffraction module according to the polarization of the polarizers ofthe input and output for several values of the parameter of conicaldiffraction, ρ₀. These light distributions were calculated using thesoftware from MMresearch Corp.

FIG. 8 is a simplified schematic illustration of a longitudinal moduleof superresolution in accordance with an embodiment of the presentinvention

FIG. 9 is a simplified schematic illustration of a method forsuperresolution algorithm of fluorophores data, in accordance with anembodiment of the present invention.

FIG. 10 is a simplified schematic illustration of the calculation ofdescriptors p.

FIG. 11 is a simplified schematic illustration of the control module ofthe platform SRCDP.

In all the figures, like reference numerals identify like parts.

DEFINITIONS AND TECHNICAL SUPPLEMENTS

The usual definitions are used for the description: phase andpolarization, polarimetry, Stokes parameters and measurement techniquesStokes parameters.

The center or centroid of a light distribution is the center of gravityof the intensity. The diameter of a light distribution is the diameterof the first zero intensity, both for regular and singular waves,without taking into account the central zero of a singular wave. Twolight distributions are collocated if their centers coincide or areseparated by a fixed, predetermined spatial value.

In this paper we use the emission wavelength, as the basic metricsystem.

In this paper, the usual definitions are used for the following opticalcomponents: lens whose definition has been broadened to include alloptical means which transmit, refract or reflect the light, auxiliaryoptics—optical sub-module to interface and adjust either the geometricparameters or the parameters of phase and/or polarization between twoother optical sub-modules or modules-, polarizer, analyzer, retardationplate, beamsplitter, polarizing and non-polarizing, beam combiner,polarizing and non-polarizing.

We refer to a partial polarizer to describe a component or a modulewhose absorption is different for the two linear polarizations—lineardichroism—or for the two circular polarizations—circular dichroism.

We refer to dynamic sub-modules of polarization or phase, to describethe optical means, which polarization or phase vary over time in acontrolled manner, discrete or continuous.

These dynamic polarization or phase sub-modules include, but are notlimited to: rotating on their axes wave plate, light valves based onliquid crystal technology, electro-optical devices, also known asPockels cells, Kerr cells, electro-optical resonant devices,magneto-optic devices, also known as cells Faraday, acousto-optic orelasto- or any combination of these means.

We refer to “centroid algorithm” to describe the standard procedure formeasuring the centroid and possibly the width (FWHM—Full width HalfMaximum) of a light distribution.

Many articles have been published on this algorithm such as the articleLindegren in 1978 (“Photoelectric astrometry—A comparison of methods forprecise picture location,” in Modern Astrometry, Proceedings of theColloquium, Vienna, Austria, Sep. 11-14, 1978, 197-217 (1978)).

In this paper, the usual definitions are used for followingoptoelectronic components: photoelectric detector, CCD, EMCCD, CMOSSPAD—Single Photon Avalanche Diode and SPAD matrix.

We use the following terms:

-   -   optical image for the spatial distribution of light intensity,    -   electronic image to describe the spatial distribution of charges        of a CCD, of current for a CMOS, of events or for a SPAD,        created by the optical image, at a given moment, in a detection        plane,    -   digital image to describe a matrix of numbers created by        conversion of the electronic image.

To simplify the reading and understanding of the text we will use theterm image to the output of a single pixel detector such as PMT or SPAD,considering it as an image consisting of a single pixel.

Where no ambiguity exists, or where the distinction between the threetypes of images is not necessary, we will use the simplified genericterm of image.

The images described in this document may be characterized asmicroimages, images of size substantially equal to a small number of theAiry disc diameters, typically less than 5 diameters, and/or low numberof pixels, typically 4*4 to 32*32.

In a digital image Aj, the indices m and n represent the indices of thepixels, and the origin of the pixels will be selected as the projectionof the center of the analysis volume defined in a later paragraph.

We presented the images using the terminology used for matrix detectors,such as CCD, EMCCD and CMOS. For SPAD and SPAD arrays the measurementresult is an ordered list in time of photons impact detailing, for eachphoton, the time of impact and the position of the impact. To simplifythe presentation of this document, we will include this case in ourdefinition of images.

Polarimetry and Stokes Vector

Polarimetry refers to the measurement of the polarization state ofincident light.

The polarization state of the incident light can be described by theStokes parameters, a set of values introduced by George Gabriel Stokesin 1852 and used in optics.

Additional technical information known to the skilled in the art

In this chapter we take a set of technical elements necessary for thedescription of the invention and known to those skilled in the art.

Cartesian and Polar Coordinates

The polar coordinates of a point, ρ, θ are deduced from the Cartesiancoordinates x, y using the equation:

$\begin{matrix}{{\rho^{2} = {x^{2} + y^{2}}};{\theta = {\tan^{1}\left( \frac{y}{x} \right)}}} & \left( {{EQ}.1} \right)\end{matrix}$

Electric Field in Polar Coordinates and Angular Modes

Given a complex electric field vector, E(ρ,θ), described in polarcoordinates (ρ, θ), the electric field can be represented by an realamplitude, A(ρ,θ), an real phase φ(ρ,θ) and a unit vector ofpolarization, u(r,θ):E(ρ,θ)=A(ρ,θ)exp[iφ(ρ,θ)]u(ρ,θ)  (EQ. 2)

It is customary in Optics to decompose the field components, i.e. itsamplitude, phase and polarization in orthogonal modes, Cartesian orpolar.

Many decompositions in orthogonal polar modes, such as Gaussian,Hermite-Gaussian and Laguerre-Gaussian modes are known to those skilledin the art.

We mainly use in this paper, the decomposition of the amplitude of theelectric field in Hypergeometric-Gaussian modes, HyGG, with thefollowing form:A(ρ,θ)∝ρ^(p+|m|)exp(—ρ² +ilθ)  (EQ. 3)

In this decomposition, ρ is the radial mode and l is the azimuthalorder.

Singular Waves

A singular wave includes a null intensity at the center and an azimuthalphase variation of a multiple of 2π. This research topic in optics,initiated by the seminal article by J F Nye and M. Berry in 1974, is nowknown as “singular optics.” Examples of regular and singular waves arepresented in the following.

Topology and Compact Light Distributions

A singular wave includes a null intensity at the center and an azimuthalphase variation of a multiple of 2_(te). This research topic in optics,initiated by the seminal article by J F Nye, et al. (“Dislocations inWave Trains,” Proceedings of the Royal Society of London, Series A,Mathematical and Physical Sciences (1934-1990) 336, 165-190(1974)).

We distinguish different families of point light distributions, ofdifferent topologies:

-   -   Regular distributions in their usual definition in Optics,    -   Singular distributions, otherwise known as optical vortices, of        topological charge (azimuthal order) i, where the phase varies        from 0 to 2πi around the direction of propagation, i being an        integer,    -   Amplitude distributions with azimuthal variation of order i,        also referred to as Laguerre-Gaussian distribution,    -   Polarization, and optionally phase distributions, with azimuthal        variation of order I, referred to as radially polarized        Laguerre-Gauss modes.

Two compact light distributions will be deemed being of differenttopological families if they meet at least one, and any of the followingconditions:

One is regular and the other is singular,

-   -   One is point-source and the other is a ring-source    -   Azimuthal orders of the amplitude of the two different light        distributions differ, —Azimuthal orders of the polarization or        the phase of the two different light distributions differ.

Alternatively, two light distributions projected onto a given volumewill be considered of different topologies if a significant portion ofthe surface illuminated together, the gradients are of reverseddirection.

The fluorophores are the best known example of the family ofpoint-source, light nanoemitters of size substantially smaller than thediffraction limit. A nanoemitter is a small secondary light emitterattached to an object, and it is significantly smaller than a fractionof a wavelength, typically but not limited to a size smaller than onefifth of the wavelength; a light nanoemitter absorbs the incident energyand re-emits light at the same wavelength as the incident light ordifferent wavelengths; the light emitted by the nanoemitter may becoherent, partially coherent or incoherent with the absorbed light. Themain examples of nanoemitters are fluorophores and nanoparticles, butalso include many other elements.

The definition in the context of the invention of nanoemitters light isdetermined by the following two conditions:

Creating a secondary point-source light emitter, and

-   -   Pre-determined positioning of the emitter with respect to a        biological or organic entity.

The physical mechanisms that can create a nanoemitter are numerous, andinclude but are not limited to absorption, scattering or reflection,fluorescence, emission-depletion, photo activation phenomena,fluorescence of two or more photons, or non-elastic scattering, Ramanscattering, or any other physical mechanisms known to those skilled inthe art. We use the term light emission to describe the emission ofelectromagnetic waves by a light nanoemitter, the light being coherent,incoherent or partially coherent.

The physical mechanisms that can create a nanoemitter are numerous, andinclude but are not limited to absorption, scattering or reflection,fluorescence, emission-depletion (S W Hell, et al., “Breaking thediffraction resolution limit by stimulated emission:stimulated-emission-depletion fluorescence microscopy,” Optics Letters19, 780-782 (1994)), photo activation phenomena (M J Rust, et al.,“Sub-diffraction-limit imaging by stochastic optical reconstructionmicroscopy (STORM),” NatMeth, 3, 793-796 (2006)), and E. Betzig, et al.(“Imaging intracellular fluorescent proteins at nanometer resolution,”Science, 313, 1642 (2006)), fluorescence of two or more photons, W.Denk, et al. (“Two-photon laser microscopy,” (Google Patents, 1991)), ornon-elastic scattering, Raman scattering, or any other physicalmechanisms known to those skilled in the art. We use the term lightemission to describe the emission of electromagnetic waves by a lightnanoemitter, the light being coherent, incoherent or partially coherent.

We refer to in this patent to descriptors of a single fluorophore todenote the set of information describing a fluorophore as a point sourceat a given moment. Since the nanoemitter is considered as a pointsource, all the information representing it contains a limited number ofparameters, namely: its position in space, its intensity, its spectralcharacteristics of the intensity, coherence, phase and polarization ofthe light emitted by the fluorophore as a function of the incidentlight.

However, in most cases, and in the description of the invention, werefer, under the designation of descriptors, a subset of descriptors ofa fluorophore including its geometric position, its intensity, and thetype of fluorophore, whether several populations of light nanoemitters,differentiated for example by their emission spectrum, are present inthe same sample. This simplification used in the description does notalter the scope of the invention which will include in its scope all thedescriptors of light nanoemitters.

To simplify the understanding of the context of the invention, thefollowing description refers only the simplest case, one in which thenanoemitter is a fluorophore and physical interaction is the one photonfluorescence. However, this description should be understood as asimplified illustration of a general description of the methods andconcepts applicable to all light nanoemitters mentioned previously orknown to those skilled in the art, regardless of the underlying physicalphenomenon.

It is striking that the nanoemitter samples the incident light intensityfield at a three-dimensional position accurately without influence ofthe complete spatial distribution of the incident intensity.

We will reference this remarkable property in this document as thesampling ability of light nanoemitter.

We refer again to the FIG. 1 ; all fluorophores positioned on a givenbiological object, 16 and 19 on the one hand and 17 and 18 on the otherhand, are referred to as “bright biological objects”, they represent amap of the biological object, in the sense defined by Alfred Korzybskiin general semantics.

We refer again to the FIG. 1 ; all fluorophores positioned on a givenbiological object, 16 and 19 on the one hand and 17 and 18 on the otherhand, are referred to as “bright biological objects”, they represent amap of the biological object, in the sense defined by Alfred Korzybskiin general semantics (A. Korzybski, et al. “Une carte n'est pas leterritoire: prolegomenes aux systemes non-aristoteliciens et a lasemantique generale” (Editions de l'Eclat, 1998)).

The luminous biological object contains information that is relevant tothe biological object, mainly spatiotemporal information, the objectposition and orientation with respect to time, and morphologicalinformation, for example in the case of division of a cell in two.

The primordial Information, the map in the terminology of generalsemantics, is the set of descriptors fluorophores and their evolutionover time. Biological and geometric information will only beextrapolations of this primordial information.

The measurement system will calculate an evaluation of the descriptorsof the fluorophores, the measured map. This measured map differs fromthe original map, due to noise, measurement conditions, the systemlimits or measurement uncertainty. This information map can be developedlater into different levels of abstraction.

The map, the basic level, therefore, comprises an evaluation of a set ofdescriptors of fluorophores, and this information may, for example, bestructured as a list of fluorophores and their descriptors. This levelof abstraction, which presents the results of direct measurement,contains a priori no biological information but is the results of aphysical measurement described by points of light, which could alsorepresent any marked entity.

The second level, the geometric level of abstraction, structuresnanoemitters in the form of geometric objects. It comprises adescription of luminous objects and their dynamic characteristics, suchas their position or orientation, or their morphology. At this level,the information is still physical and geometric information describing aset of objects. The geometrical information uses the measured card andauxiliary information, potentially external to the system, the relationbetween light spots and objects.

The biological level of abstraction, allows some understanding of thebiological reality through a constitutive relationship between objectsmeasured and corresponding biological entities. It contains a set ofinformation on the biological object, mainly the position and itsdynamics, its shape and morphology. The biological information uses themeasured card and the geometrical information and auxiliary information,potentially external to the system, the relation of the light spots andobjects with biological entities. A number of conclusions on thebiological functionality of the sample can be obtained at this level.

Conical refraction is an optical phenomenon predicted by Hamilton in1832, and two months later confirmed experimentally by Lloyd. Conicalrefraction describes the propagation of a light beam in the direction ofthe optical axis of a biaxial crystal. Hamilton predicted that the lightemerges in the form of a hollow cone of rays. Conical refraction is animportant phase in the history of science and has played a role in thedemonstration of the theory of electromagnetic waves.

Conical refraction is an optical phenomenon predicted by W. R. Hamiltonin 1832 (“Third Supplement to an Essay on the Theory of Systems ofRays,” Trans. Royal Irish., Acad., pp 1-144 (1833)), and two monthslater confirmed experimentally by Lloyd (“On the Phenomena presented byLight in its Passage along the Axes of Biaxial Crystals”, The London andEdinburgh Philosophical Magazine and Journal of Science ii, 112-120(1833), and “Further Experiments on the Phenomena presented by Light inits Passage along the axes of Biaxal Crystals”, The London and EdinburghPhilosophical Magazine and Journal of Science H, 207-210 (1833)).Conical refraction describes the propagation of a light beam in thedirection of the optical axis of a biaxial crystal. Hamilton predictedthat the light emerges in the form of a hollow cone of rays. Conicalrefraction is an important phase in the history of science and hasplayed a role in the demonstration of the theory of electromagneticwaves.

A renewed interest in the conical refraction occurred in the last yearsof the twentieth century has led to a complete theory by M. V. Berry, etal. (“Conical diffraction asymptotics: fine structure of Poggendorffrings and axial spike,” Journal Of Optics A-Pure And Applied Optics, 6,289-300 (2004)), Berry, et al. “Conical diffraction complexified:dichroism and the transition to double refraction,” Journal Of OpticsA-Pure And Applied Optics, 8, 1043 (2006), and Berry, et al, “Chiralconical diffraction,” Journal Of Optics A-Pure And Applied Optics 8, 363(2006)), validated experimentally in 2009 (C. Phelan, et al,

-   -   “Conical diffraction and Bessel beam formation with a high        optical quality biaxial crystal,” J. Opt. A, Pure Appl. Opt, 7,        685-690 (2009)). Here we follow the theory, terminology and        definitions of Berry, including, from this point, the name        change of the physical effect, using the more rigorous term of        conical diffraction.

Conical diffraction has attracted considerable theoretical andexperimental, but “no practical application seems to have been found,”(MV. Berry, et al., “Conical diffraction: Hamilton's diabolical pointsat the heart of crystal optics,” Progress in Optics 50, 13 (2007)).

Other effects exist, creating inherently weaker conical diffractioneffects or creating conical diffraction along a short optical path.These effects include polymers, liquid crystals and induced externallybirefringence effects. The polymers include but are not limited to:stretched polymer sheets and cascade polymerization, liquid crystalsinclude but are not limited to: thermotropic biaxial nematic phase, theexternal effects induced birefringence include, but are not limited to:applying an electric field creating an electro-optical effect on anon-centrosymmetric cubic crystal, and the photo-elastic modulator.

Other effects exist, creating inherently weaker conical diffractioneffects or creating conical diffraction along a short optical path.These effects include polymers, liquid crystals and induced externallybirefringence effects. The polymers include but are not limited to:stretched polymer sheets and cascade polymerization (A. Geivandov, etal. “Printable Thin Film birefringent Retarders for LCD”). Liquidcrystals include but are not limited to thermotropic biaxial nematicphase (B. Acharya, et al. “Biaxial Nematic Thermotropic The ElusivePhase in Rigid Bent-Core Molecules,” Pramana 61, 231-237 (2003)); theexternal effects induced birefringence include, but are not limited toapplying an electric field creating an electro-optical effect on anon-centrosymmetric cubic crystal (T. Aldonado, “Electro-opticmodulators,” in Handbook of Optics, M. Bass, ed. (McGraw Hill, Orlando,1995)); and the photo-elastic modulator (J. Kemp, “Piezo-OpticalBirefringence Modulators: New Use for a Ion-Known Effect,” Journal ofthe Optical Society of America 59, 950-953 (1969)).

Referring now to FIG. 3 , incident light, 30, is assumed to be parallel,although other conditions can be adapted using simple optical means. Thesetup itself comprises a first lens 31, a conical crystal 32 and anoptional lens 33. The first two lenses 31 and 33 are preferablyconfigured in the form of a Kepler telescope 1:1. The numerical apertureof the first lens 31 in the image space, represented below by U_(o),determines the parameters of the conical diffraction effect through theconical radius, defined below. An imaging plane conical, 35, is placedin the focal plane of the first lens 31, a partial polarizer part 29,described above, may also be added. A focusing lens, 36, determines thescale of the final light spot. It can be a microscope objective externalor can be merged with the second lens 33, as implemented in anotherembodiment of this invention. The distribution of the light projectedonto the sample is in a first approximation, neglecting the vectorialeffects, a reduced image of the light distribution in the image plane.The influence of vectorial effects will be discussed below. The scaleratio is determined for a microscope objective by the magnification.

The spatial variable, R, the conical imaging plane, and the wave vector,U, are represented by cylindrical coordinates R, θ_(R) et U, θ_(U). λ isthe wavelength of light.

The behavior of the electric field emerging from the conical crystal 32is fully characterized by a single parameter, the radius conical R₀; theconical radius depends on the material and geometrical characteristicsof the crystal, as defined in [Berry, 2004].

We introduce standardized parameters for the description below of thelight distribution, to be valid in both conical imaging plane and at thefocus of the microscope objective, in the limits of the scalar theory ofdiffraction.

The normalized radial position, ρ, the wave vector normalized, u,represented by cylindrical coordinates par ρ, θ_(R) et u, θ_(U), and thenormalized radius conical ρ₀ are given by:

$\begin{matrix}{{\rho = {2\frac{R}{\lambda}U_{0}}},{{u = \frac{U}{U_{0}}};{\rho_{0} = {2\frac{R_{0}}{\lambda}{U_{0}.}}}}} & \left( {{EQ}.4} \right)\end{matrix}$

U₀ being the numerical aperture of the system. For ρ₀<2, we refer hereto a thin conical crystal, for ρ₀<<1, we refer here to the form of alinear thin conical crystal and for ρ₀<0.5 to a thin sinusoidal conicalcrystal.

The wave emerging crystal thin conical, E(ρ, θ_(R)), expressed innormalized coordinates, is constituted by the superposition of twowaves, referred to herein as the fundamental wave, E_(F) (p), a regularwave, and vortex wave, E_(V) (ρ,θ_(R)), a singular wave; these two wavesare coherent one with another, collocated, and circularly polarized withan inverse direction of chirality:

$\begin{matrix}{{E\left( {\rho,\theta_{R}} \right)} = {{{E_{F}(\rho)} + {E_{V}\left( {\rho,\theta_{R}} \right)}} = {{{E_{F}(\rho)}\begin{pmatrix}1 \\{- i}\end{pmatrix}} + {{F_{V}(\rho)}{\exp\left( {{- i}\theta_{R}} \right)}\begin{pmatrix}1 \\i\end{pmatrix}}}}} & \left( {{EQ}.5} \right)\end{matrix}$

In this equation, E_(F) (ρ) is the scalar fundamental amplitude, F_(v)(ρ) is the reduced scalar magnitude of vortex and they are given by:E _(F)(ρ)=2π∫du u cos(ρ₀ u)J ₀(ρu);F _(v)(ρ)=2π∫du u sin(ρ₀ u)J₁(ρu).  (EQ. 6)

For a thin linear conical crystal, the fundamental wave can beapproximated by an Airy disk and the vortex wave can be approximated toa linear vortex, represented by:F _(v)(ρ)=2πρ₀ ∫du u ² J ₁(ρu).  (EQ. 7)

Assuming that the action of partial polarizer, 29, is the scaling of thevortex wave by a parameter a, the Stokes parameters can be deduced fromthe above equations:S ₀=(E _(F)(ρ))²+(α² F _(v)(ρ))²S ₁=2αE _(F)(ρ)F _(v)(ρ)sin θ_(R) ;S ₂=2αE _(F)(ρ)F _(v)(ρ)cos θ_(R);S ₃=(E _(F)(ρ))²−(α² F _(v)(ρ))²β=θ_(R);  (EQ. 8)

We use the terms of “sparse object” to describe a set of light emittingpoint like emitters, of a number less than twelve, positioned in avolume whose size in each dimension is less than 3 wavelengths, at thewavelength of transmission or at the wavelength of the reflection of theemitters. The volume of a size less than 3 wavelengths that contains thesparse object is referred to as a analysis volume of reduced size.

We refer now to FIGS. 4 a to 4 c , which are a simplified representationof the concept of volumic containment in the confocal microscope.

The functionality of the volumic containment is limited in all threespatial dimensions, the observed region of the sample volume to a sizeas small as possible, analysis volume. The functionality of the volumiccontainment limits the analysis volume by the combination of twoeffects: the confinement of the light projected onto a small area,ideally the size of the Airy spot, 50, and the elimination of defocusedlight by the confocal hole, 28, of FIG. 2 . The superposition of thesetwo effects creates a small volume, the analysis volume, 60. This volumedetermines the size of the elementary cell detected by the system.

Consider a sparse object, 51, consisting of a plurality of fluorophores,53 to 59. The fluorophores from 53 to 55 positioned in the test volume60, and only they are both excited by the light source and the photonsemitted by them arrive at the detector module. The fluorophores notlocated in the cone of illumination, 56 and 57 are not illuminated bythe incident light. The light emitted by the fluorophores 58 and 59,located at the conjugate plane of the confocal hole, 28 of FIG. 2 , isblocked almost entirely by the confocal hole, 28 FIG. 2 .

Two different Cartesian coordinates are defined in the system, FIG. 4 c:

The reference “i”: The axes referenced “i” represent a Cartesianreference system centered on the center of the analysis volume, 61.

The reference “a”: the axes referenced “a” represents a Cartesianreference centered for each light nanoemitter on the nanoemitterconsidered as a discrete point, 62.

When using the PSIT method, described later, if a vortex is projected onthe sample, the center of the vortex will be generally defined as thecenter of the analysis volume.

The confocal microscope limit the analysis volume using the volumicconfinement described above. The volumic confinement volume is obtainedby the combination of two effects: confinement of the light projected ona small surface, ideally of the size of the Airy disk, 50, and removalof defocused light by the confocal hole, 41. The superposition of thesetwo effects creates a small volume, the analysis volume 60. This volumedetermines the size of the elementary cell detected by the system.

At least one embodiment of the invention uses conical diffraction torealize the fundamental optical modules of the technique. However,alternative implementations, replacing the modules based on conicaldiffraction by modules based on other optical concepts, are able toprovide the same functionality. They are part of the scope of thisinvention. Alternative optical concepts include but are not limited touniaxial crystals, subwavelength gratings, structured laser modes,holographic components and other techniques known to the skilled in theart.

These concepts, techniques and optical and optoelectronic devices areknown to those skilled in the art and all such optical means aredescribed in numerous publications such as the book written by D.Goldstein, “Polarized Light”, Pawley, “Handbook of Biological ConfocalMicroscopy,” Bass, “Handbook of Optics”, and many other publicationsknown to those skilled in the art.

Acronyms

We use in this paper the acronym, SRCD, “Super Resolution using Conicaldiffraction” to name the platform, modules and systems specific to thepreferred implementation of this invention.

We use in this paper the acronym PSIT “Projected Sequence of Intensitieswith various topologies”

We use in this paper the acronym, PDOS, “Position Dependent OpticalSemaphore”.

The SRCDP platform, “Conical diffraction using Super ResolutionPlatform” is a platform for microscopy, implementing the measurementmethodology and using optical modules based on conical diffraction.

SRCDP platform is the preferred implementation of the measurementmethodology. We use in this paper the acronym LatSRCS to name theoptical module implementing the PSIT method for the preferredimplementation of this invention.

We use in this paper the acronym LongSRCS to name the optical moduleimplementing the preferred implementation of the method PDOS of thisinvention.

Some embodiments of the present invention comprise a new measuringmethodology; the measurement methodology, and a coherent set of systemicand algorithmic method, hardware tools, software tools and algorithmsfor its implementation

The measurement methodology according to embodiments allows acquisitionof nanosized optical data and image superresolution.

The measurement methodology is primarily, but not exclusively, used forthe measurement of super-resolved biological samples data marked withfluorophores.

The measurement methodology can be implemented using the differentmethods of measurement and processing algorithms, described below.

Among other things, the measurement methodology can be implementedtogether or separately using two new measurement methods, referred toas:

-   -   PSIT Projected Sequence of Intensities with various Topologies,”        and    -   PDOS, “Position Dependent Optical Semaphore”.

Some embodiments of the invention also relate to a system—a platform formicroscopy—implementing the methodology of measurement using themeasurement methods PSIT and PDOS. This system, the SRCDP platform,“Conical diffraction based Platform Super Resolution” is the preferredimplementation of the measurement methodology.

These concepts, techniques and optical and optoelectronic devices areknown to those skilled in the art and all such optical means aredescribed in numerous publications such as the book written by D.Goldstein, et al. (“Polarized Light” (CRC, 2003), Vol. 83). The“Handbook of Microscopy Confocal”, J B Pawley, (Springer Verlag, 2006).“Handbook of Optics”, M. Bass, (McGraw-Hill, 2001)) and many otherpublications known to those skilled in the art.

Additionally, the SRCDP platform includes an improved detection module,a control module of the system, and software support.

The measurement methodology comprises using both measurement methods,the methods PSIT and PDOS. However, in some applications, the use ofboth methods may not be necessary, we will refer in this case to thesimplified measurement methodology, which is part of the scope of thisinvention.

Some embodiments of the invention also relate to methods of using themeasurement methodology for measuring distribution of fluorophores andfluorophores, and monitoring in two or three dimensions of fluorophores.

In addition, certain embodiments of the invention relate to a largenumber of variants of implementations of the methodology and methodsPSIT and PDOS, platform SRCD, optical modules and LatSRCS LongSRCS andalgorithmic SRCDA.

The functionality of the confocal microscope described by Minsky, andexplained previously, is limiting in three spatial dimensions, theobserved region of the sample volume to a size as small as possible, thevolume analysis.

The functionality of the confocal microscope described by M. Minsky(“MicroscopyApparatus,” (Google Patents, 1961)) and explainedpreviously, is limiting in three spatial dimensions, the observed regionof the sample volume to a size as small as possible, the volumeanalysis.

Referring now to FIG. 4 d , which is a simplified conceptualrepresentation of the paradigm of the measurement methodology accordingto at least one embodiment of the invention. The paradigm of thismethodology is much more ambitious than that of the fluorescenceconfocal microscope, shown schematically in FIG. 4 a.

In FIG. 4 d , a test volume 60 is created at the focal plane of themicroscope objective, 22; it contains a sparse object, 51, consisting ofseveral fluorophores, 53 to 59; the result of the system implementingthe method is a reconstructed sparse object, 63, a list of fluorophoresand a list of their attributes, 64.

A system implementing the method according to at least one embodiment ofthe invention is capable of recovering independently and accurately theattributes of several fluorophores in a luminous volume of dimensionssimilar to those of confocal microscopy. To achieve this goal, themethodology according to some embodiments of the invention is designedto create optically for each illuminated volume, a large amount ofinformation in both time and spatial domains.

The most developed process of the measurement methodology, according toan embodiment of the invention, can be segmented into seven steps, fiveoptical steps, an optoelectronic detection step and an algorithmic step.

Optical Steps:

-   -   Projection of a sequence of compact light distribution of        different topologies on the analysis volume    -   Emission of fluorescent light by fluorophores Imaging of        fluorophores in the focal plane    -   Separation of the reflected light detected in several        independent channels simultaneously and/or sequentially    -   Optional limitation in the focal plane of the analyzed light        Detecting Step

Detecting the light intensity by one or more point like or matrixphotodetectors.

Algorithmic Step:

-   -   Reconstruction of the list of fluorophores, constituting the        sparse object, and their attributes from the set of the detected        images,

According to another embodiment of the present invention, themeasurement methodology consists in the realization of optical steps,previously described and omitting either the first is or the fourthoptical step.

The compound optical process that implements the methodology comprises:performing a series of optical measuring processes, controlled by thecontrol module of the system, by varying the sequence of illuminationand/or the functionality of the channels and/or the position of thesequence illumination as function of measured data or of externalinformation. An example of compound optical process implementing themethodology according to an embodiment of the invention will be detailedbelow.

The intermediate result, the raw information is obtained at the end ofthe detection step. Raw information comprises a set of images A_(op)(m,n) representing for the o light distribution, the image from thedetection channel p.

As in a confocal microscope, the measurement process analyzes a smallvolume in a much larger object. It will therefore require the additionof additional modules, similar to those of a confocal microscopeincluding a scanning process, a software module integration, analysisand visualization of data points in surfaces and/or three-dimensionalobjects.

A method of measurement PSIT according to one embodiment of theinvention, projects a sequence of light distributions of differenttopologies, on the analysis volume.

The measurement method PSIT, performs the following functions:

-   -   Projection of a sequence, the emission sequence of compact light        distributions of different topological families on a sample, and    -   For each compact light distribution:        -   Emission of light by fluorophores on the sample,        -   Creation, by means of the microscope optics, of an optical            image,        -   Acquisition of the optical image on a photodetector and            creation of a digital image.

In more detail, it is noted that:

The transmission sequence comprises at least two point like lightdistributions, of different topological families

The transmission sequence is projected onto a biological sample labeledwith fluorophores which are referenced as light nanoemitter.

The light emitted, emerging from each light nanoemitter, is dependentfor each nanoemitter of the light intensity, in the incoherent case oron the electromagnetic field, in the coherent case, incident on thethree-dimensional spatial position of the light nanoemitter, theaforesaid light sampling property of the nanoemitter discussedpreviously.

For each light distribution pattern of the transmission sequenceprojected on the sample, an optical image is created.

The set of images corresponding to all the light distributions of thetransmission sequence is referred to as the sequence of images.

The PSIT method according to this embodiment can acquire mainly lateralinformation, that is to say, the lateral position of each of thefluorophores.

In a preferred embodiment, the PSIT method is implemented by theprojection of light distributions of different topologies created byconical diffraction and modified by a variation of the polarizationstates of input and output.

A PDOS method according to an embodiment of the invention includes thedistribution of an “optical semaphore” of the light reemitted by thefluorophores between at least two detectors.

Ideally, the function of the optical semaphore is to separate differentareas of the test volume on different detectors. Practically, theoptical semaphore creates, for each detector, a transfer function of thelight emitted by a light nanoemitter, depending on the position in spaceof the light nanoemitter and different for the different detectors.

In a preferred embodiment, the PDOS method is implemented to separate ondifferent detectors the collimated light, emerging from fluorophorespositioned at the focal plane of the lens, from non-collimated lightemerging from fluorophores lying within or beyond the focal plane.

The PDOS method, in its preferred embodiment, allows acquiringessentially longitudinal information, that is to say, the longitudinalposition of each of the fluorophores.

Mathematically, the method according to some embodiments of theinvention provides a transfer function converting the spatialdistribution of the fluorophores in space in unprocessed informationconsisting of a set of images. The algorithmic performs the inverseoperation: it reconstructs the spatial distribution of the fluorophoresin space from the set of images in the unprocessed information.

In mathematical terms the algorithm solves an inverse problem orparameter estimation. The model equations are known and the number offluorophores in a sparse object is a-priori limited. 11 the mathematicalprocedures known to those skilled in the art can be used for solvinginverse problems and parameter estimation. We describe later an exampleof algorithm adapted specifically to the measurement methodologyaccording to an embodiment of the invention.

In addition, we present, for its symbolic value, a new solution to theproblem of discrimination of two points located at a small distance fromeach other. This problem studied by Lord Rayleigh, is the base of theresolution criterion in many areas of Optics.

It has thus been described, rather broadly, the characteristics of theinvention in order that the detailed description thereof may be betterunderstood, and in order that the present contribution to the art may bebetter appreciated. Many additional features of the invention will bedescribed below.

The preferred implementation of the method according to one embodimentof the invention is a hardware platform and algorithms, referred to asthe SRCDP platform, 500, shown in FIG. 5 .

The SRCDP platform, 500, implements the method according to anembodiment of the invention, by combining the two methods PSIT and PDOSabove.

The platform SRCDP observed, FIG. 5 , a biological sample, 11, includinga plurality of fluorophores. The result of the observation of thebiological sample by the SRCDP platform is the acquisition ofsuperresolution information, representative of the observed sample.

The platform SRCDP, 500, as shown in FIG. 5 , includes mainly:

In its hardware part:

-   -   A confocal microscope 200, adapted or optimized, similar to the        confocal microscope, described previously, and including all        appropriate components, as previously described    -   Two new and complementary optical modules, mounted on a standard        microscope. The two new optical modules are optical modules        LatSRCS, 700, and LongSRCS, 800, described in detail later with        reference to FIGS. 6 and 8 , respectively. The optical module        700 LatSRCS, implements the steps of illumination required for        implementing the PSIT method according to one embodiment of the        invention. The optical module LongSRCS, 800, implements the        steps of the light intensity distribution in a plurality of        emerging Images of the PDOS method according to an embodiment of        the invention and;    -   Module algorithmic SRCDA, 600, which will be described by        referring to FIG. 8 , is able, to reconstruct superresolution        information of the biological sample from images created by the        platform SRCDP.    -   Other auxiliary elements, such as computer 66 and software 67,        necessary for the realization of the platform.        LatSRCS Optical Module Implementing the PSIT Method

We describe, with reference to FIG. 6 , an optical module according toan embodiment of the invention, the optical module LatSRCS, 700, and itsspecific function in microscopy.

The optical module LatSRCS, 700 according to this embodiment is anoptical module, projecting on a plurality of fluorophores in a sample, asequence of compact light distributions of different topology. Eachfluorophore fluoresces with a sequence of fluorescent light intensitiesdependent on the incident intensity on the fluorophore andcharacterizing the lateral position of the fluorophore. In mostembodiments, the light compact distributions of different topologies arecreated by interference with variable amplitudes and phases between anordinary wave and singular wave. In the preferred embodiment, theregular and singular waves are created by a thin conical crystal.

The optical module LatSRCS, 700, is positioned in the illumination pathof the confocal microscope 200; it projects a sequence of compact lightdistributions of different topologies on the sample 11 using theconfocal microscope objective 200. In the preferred embodiment using theconical diffraction, the incident intensity at a specific position onthe sample 11 will be proportional for each light distribution pattern,to a specific combination of the Stokes parameters.

The optical module LatSRCS, 700, uses an inherent feature describedabove, specific to the fluorophore, which samples the intensity of lightincident on its precise position (the fluorophore), and reemitsfluorescent light dependent on the incident light. It is remarkable thatthe measured information is directly related to the position of thefluorophore in the compact light distribution, relayed by the Stokesparameters. This information is frozen by the functionality of thefluorophore, its ability to absorb and re-emit light, breaking theoptical chain. This information is carried by the fluorescent light asan emerging light distribution recoverable by a detector assembly 65.

If the incident light varies temporally according to a sequence ofcompact light distributions of different topologies, the intensity ofthe fluorescent light reemitted varies in the same proportions. Thesequence of the re-emitted fluorescent light is proportional to thesequence of compact light distributions of different topologies. Fromthis information, it is possible to retrieve the position of thefluorophore, as explained below.

The PSIT method, according to embodiments of the invention, refers tothe projection of a sequence of compact light distributions of differenttopologies in a microscope, the interaction with fluorophores,collecting the reflected light by the objective of microscope, 22,detecting the fluorescent light by the improved detector assembly 65,and the analysis of the information by a suitable algorithmin someembodiments, the improved detection assembly, 65, comprises a singledetector, and recovers only the overall intensity as a function of time,while in other embodiments the improved detection assembly comprises asmall area of pixels and recovers also the spatial distribution of thefluorescent light. All retrieved information consisting of a pluralityof images, the named as lateral superresolution images.

In a preferred embodiment, the contribution of a fluorophore in theilluminated volume positioned in a specific lateral superresolutionimage is proportional to a specific combination of the Stokes parametersof the incident light at the fluorophore position.

Lateral superresolution images, the information created by compact lightdistributions of different topologies, is new and was not present in theprior art. This new information helps to refine the position of thefluorophores, to quantify the number of fluorophores present in theilluminated volume and to differentiate multiple fluorophores present inthe same volume.

We refer now to FIG. 6 , which is a simplified schematic illustration ofan optical module LatSRCS, 700 in accordance with an embodiment of thepresent invention.

FIG. 6 shows an optical module LatSRCS, 700; it includes all thecomponents of the module of conical diffraction, of FIG. 3 , which areimplemented in the same way as in the module 300 of conical diffraction.The optics of the light source of the scanning confocal microscope isassumed to be infinite conjugate, although other conditions can beadapted using auxiliary optics. The incident light entering from thelight source is parallel, 30. The optical module itself, 700, comprisesa first lens 31, a conical crystal 32, and a second lens 33; a partialpolarizer, 29, described above, may also be added. The first two lenses31 and 33 are preferably configured in the form of a Kepler telescope ofratio of 1:1; the conical imaging plane, 35, is placed in the commonfocal plane of the lenses 31 and 33. The numerical aperture of the firstlens, 31, determines the parameters of the conical diffraction effectthrough the conical normalized radius, defined below. The secondobjective 33, restores the parallelism of the light, to inject it in themicroscope. It further comprises a sub-module of polarization control71, including, for example, a rotating quarter-wave plate, a pair ofliquid crystal light valves or a Pockels cell, 72 and an analyzer 73.The information of the Stokes parameters can be converted into sequenceinformation, through a sequence of light distributions spatiallydifferentiated and carrying sequential information, as described above.

Referring to FIG. 7 a , this figure shows the light distribution,created through a conical crystal with a normalized conical parameter ρ₀of 0.388, calculated by a scalar approximation for different input andoutput polarization states. These light distributions were calculatedusing the software Diffract from MMresearch Company. These lightdistributions were calculated in an imaging intermediate plane and notat the focus of the objective to separate the conical refraction [shouldbe diffraction] effects from vectorial effects. The—input andoutput—states of polarization are characterized by their angle forlinear polarizations and their chirality for circular polarizations.

Referring to FIG. 7 b , this figure shows the light distribution,created through a conical crystal with a normalized conical parameter ρ₀of 0.818, calculated by a scalar approximation for different input andoutput polarization states. These light distributions were calculatedusing the software Diffract from MMresearch Company. These lightdistributions were calculated in an imaging intermediate plane and notat the focus of the objective to separate the conical refraction [shouldbe diffraction] effects from vectorial effects. The—input andoutput—states of polarization are characterized by their angle forlinear polarizations and their chirality for circular polarizations.

We denote mainly the following light distributions:

-   -   The fundamental, FIG. 7 a ₀₀ and FIG. 7 a ₁₁ obtained between        parallel circular polarizers, which is a distribution close to        the Airy distribution,    -   The vortex: FIG. 7 a ₀₁ and FIG. 7 a ₀₁ obtained between crossed        circular polarizers,    -   The distribution that we called the “crescent moon”        distribution; the subfigures 7 a _(0,2-5), 7 a _(1,2-5), 7 a        _(2-5,0) et 7 a _(2-5,1), are obtained between a circular        polarizer and a linear polarizer with a variable angle. This        distribution is antisymmetric and the axis rotates following the        linear polarizer axis,    -   The distribution that we called the “half-moons” distribution;        the subfigures FIGS. 7 a ₄₂, 7 a ₃₅, 7 a ₂₄ et 7 a ₅₃ are        obtained between two crossed polarizers; this distribution is        symmetric,    -   The more complex light distributions, FIG. 7 b , for a crystal        with a normalized conical parameter, ρ₀, greater than 0.5,    -   The creation of additional light distributions using two—or        more—crystal cascading conical crystals (not shown) with or        without static or dynamic polarizing elements between the        crystals.        Redundancy and Random Phase Variations

The elementary light distributions described in FIG. 7 can be obtainedin several ways. In addition, some of them can be obtained as a linearcombination of other elementary light distributions, e.g. the vortex canbe obtained by the sum of any two orthogonal “half-moons” lightdistributions.

This redundancy allows some averaging of random phase errors inevitablypresent in many measurement process of biological objects. Thisreinforces the robustness of the measurement methodology of theembodiments of the invention and its applicability.

New light distributions can also be obtained as mathematicalcombinations of elementary light distributions. The “pseudo-vortex”,light distribution, calculated from arithmetic combinations of the fourdistributions Stokes has the feature of having a strong gradient at theorigin.

Method PS1T was originally designed to allow lateral superresolution,however PS1T method can also be used to obtain the longitudinal positionof a fluorophore. Indeed, some elementary light distributions arerelatively insensitive—within reasonable limits—to a variation of thelongitudinal position of the fluorophore, others are rather sensitive. Asequence of compact light distributions, some of them independent andsome of them depend on the longitudinal position would reveal thelongitudinal position of fluorophores.

In addition for the light distributions which are highly dependent onthe longitudinal position of the fluorophore, a series of elementarylight distributions slightly shifted longitudinally, one relative to theother can be projected on the sample, allowing a set of imagescontaining longitudinal information.

In addition, some more complex elementary light distribution, consistingof more complex overlapping of waves with a strong longitudinaldependence exist, eg the “three-dimensional dark spot” described byZhang, which create a black spot surrounded in three dimensions by aluminous sphere. As described by Zhang, “Investigation and applicationsof the three dimensional (3D) dark spot surrounded by a light shell inall directions have attracted a great deal of attention. Insuperresolution fluorescence microscopy, a 3D dark spot is used as theerase beam”. These “three dimensional dark spots” consist of asuperposition of Laguerre-Gauss functions, which can be achieved withina laser cavity or using a hologram or a phase plate, as suggested byZhang, or using uniaxial or conical crystals as suggested by theinventor.

In addition, some more complex elementary light distribution, consistingof more complex overlapping of waves with a strong longitudinaldependence exist, eg the “three-dimensional dark spot” described byZhang (“Generation of three-dimensional dark spots with a perfect lightshell with a radially polarized Laguerre—Gaussian beam,” Applied optics,49, 6217-6223 (2010)), which create a black spot surrounded in threedimensions by a luminous sphere. These “three dimensional dark spots”consist of a superposition of Laguerre-Gauss functions, which can beachieved within a laser cavity or using a hologram or a phase plate, assuggested by Zhang, or using uniaxial or conical crystals as suggestedby the inventor.

Vector Effects

The theory developed so far describes the light distribution in theimaging plane of the microscope 35. The distribution of the lightprojected onto the sample is, according to the theory of the geometricalimaging, a reduced image of the light distribution in the image plane.

However, as described extensively in the literature, for a highnumerical aperture objective, the imaging geometric theory is notaccurate and vector effects must be taken into account. These effectsconsist essentially in the presence of a component, longitudinallypolarized.

Referring again to FIG. 6 , to mitigate vector effects, it may beadvantageous to maintain the final analyzer fixed and to add anadditional element, fixed or variable, the output polarizationadaptation submodule, 74, for controlling the output polarization. Wefound that an output polarization with circular symmetry greatly reducesthe effects vector. Such polarization can be circular, radial orazimuthal. For circular polarization, the output polarization adaptationsubmodule, 74, is simply a quarter wave retardation plate. In this case,the elements of longitudinal polarization have vortex symmetry andintegrate harmoniously into the system with only a small change in theform of the Stokes parameters, even for microscope objectives with highnumerical aperture.

Alternatively, the output polarization adaptation submodule, 74, may bevariable and adapted to the topology and the symmetry of each of thecompact light distribution.

LongSRCS Optical Module Implementing the PDOS Method

We describe below an optical module LongSRCS with more details. Thesystem of longitudinal superresolution, according to an embodiment ofthe invention, channels the incident light intensities of a plurality ofpoint sources located in a small illuminated volume, either on separatedetectors or on distinct geometric positions on the same detector or ona combination of both, as function of the spatial position of each pointsource.

In simpler words, the intensity emitted by a fluorophore positionedlongitudinally at the point A will be physically separated from theintensity emitted by a fluorophore positioned longitudinally to point B.

The optical module LongSRCS, according to an embodiment of theinvention, allows the separation in volume slices, different slices ofthe illuminated volume being physically separated on different sets ofdetectors.

In the preferred embodiment, which will be explained below, the opticalmodule LongSRCS separates an illuminated volume in at least threeadjacent slices, separating the middle slice from of the other twoslices on sets of independent improved detectors, and creating a spatialdifferentiation between the two remaining slices on the same set ofimproved detectors.

We refer now to FIG. 8 , which is a simplified schematic illustration ofa LongSRCS optical module, 800, according to an embodiment of thepresent invention.

The optical module LongSRCS channels the incident light intensity of aplurality of point sources located in a small volume of light, either onseparate detectors or on distinct geometric positions on the samedetector either a combination of both, depending on the longitudinalposition of each point source.

In a preferred embodiment, it operates on the fluorophores, representedby 80, 80′ or 80″, according to their longitudinal position. Itcomprises a first collimating lens 81, which may consists, in someembodiments of the microscope objective 4.

The fluorophore 80 is positioned in the focal plane of the collimatinglens 82, the light from the fluorophore 80, emerging from thecollimating lens 81 is collimated.

The fluorophores 80′ and 80″ are placed before and after the focal planeof the collimating lens, 82, at a distance of ±Δz, the light from thefluorophores 80′ or 80″ emerging from the collimating lens 81 beingconvergent or divergent.

The LongSRCS optical module includes a polarization beam separator,shown in FIG. 8 , in the form of a lateral displacement polarizationbeam splitter, 83. The polarization beam splitter splits the incidentlight, assumed to be non-polarized in two polarization channels, 84 and85, having orthogonal linear polarizations. The system can be simplifiedby using a single polarization channel instead of two, if the incominglight is already polarized or at the cost of a loss of half of theintensity of the incident light, for unpolarized light.

Two quarter waveplates, 86 and 87, transform, for each channel, thelinearly polarized circular polarizations.

A conical crystal is placed in each of the channels 88 and 89. In eachchannel, a conical diffraction setup, as described in the FIG. 3 , isconstituted by the collimator lens 81, acting as a primary objective ofthe setup of conical diffraction, 31, and a conical crystals, 88 and 89.Conical diffraction pattern will be complemented by a second lens 33, inthe following.

For the fluorophore, 80, positioned in the focal plane of thecollimating lens 82, the light emerging from the collimator lens 81, is,as discussed above, collimated; referring to the setup of conicaldiffraction, the Numerical Aperture of the collimating lens 81, in theimage space, and the normalized radius cone are zero, so that the effectof conical diffraction on the beam from the fluorophore 80 is zero.Therefore, the conical crystal does not change the geometry of thefluorescent light emitted by the fluorophore, or its polarization, whichremains circular with the same chirality.

For fluorophores, 80′ or 80″, which are not positioned in the focalplane of the collimating lens 82, the light diverges or converges;Referring again to setup conical diffraction described above, theNumerical Aperture in the image plane of the collimating lens 81, whichis equivalent to the first lens of the conical diffraction setup, 31, isnon-zero. For a given value Δz defocus, positive or negative, most ofthe light emerging from the crystal is contained in the conical wavevortex, which has a form of a vortex, and is inverted chirality.

The functionality of the conical diffraction setups positioned in eachof the channels is to distinguish the collimated light from the lightconverging or diverging by reversing the chirality of the circularpolarization of the light for converging or diverging light.

Two other blades quarterwave plates, 90 and 91 transform the circularpolarizations, emerging each channel, linear polarizations. We refer,for each channel, to the linear polarization, which would have emergedfrom the retardation plate, if the crystal had been removed, as thepolarization of collimation

The optical module comprises a LongSRCS combiner/separator of fourports, shown in FIG. 8 as a lateral separation four portscombiner/separator 92.

For each channel it separates the two polarizations, and merges the twopolarizations of collimation in the same path, the path of collimation,93, and the polarized light orthogonal to the collimation polarizationin another path, the path of non-collimation, 94. The directions of theaxes of the quarterwave plates, 86, 87, 90 and 91 must be chosenappropriately. The combined beams do not interfere, because they comefrom originally unpolarized beam.

The incident light into the path of collimation is focused onto thedetector of collimation, 96, using the focusing lens of the collimatingpath, 95, which behave functionally as the second lens, 32, of theconical diffraction setup.

In the path of non-collimation, an additional lens 97 is inserted, andthe additional lens 97, together with the collimating lens, 81, createsa new lens system, 98, whose focal plane, 99 is positioned at adifferent position of the focal plane of the collimating lens 82, theposition of the fluorophore 80′. An additional quarter waveplate, 100,cancels the action of the quarter waveplates, 90 or 91, turning back theincoming beams of each of the channels of polarization, to the circularpolarization, which they were at the output polarized crystals conical,88 or 89.

An additional conical crystal, 101, is added in the way ofnon-collimation as a third conical diffraction setup—the auxiliaryconical diffraction setup—with the system of lenses 98, acting as thefirst lens of the conical diffraction setup, 31.

The fluorophore 80′ have been positioned before the focal plane of thecollimating lens, 82, at a distance of Δz, but, relative to the lenssystem 98, it is positioned at the focal plane 99. The light from thefluorophore 80′ had already been converted into a vortex by one of theconical diffraction setups consisting of the collimating lens 81, andone of the conical crystals 88 or 89, depending on the channel ofpolarization traveled by the light. The light from the fluorophore 80 iscollimated at the output of the lens system, 98, after the additionallens, 97.

Referring to the new conical diffraction setup, the numerical apertureof the lens system in the image space, and the normalized conical radiusare zero for fluorophore 80; the effect of conical diffraction, of theauxiliary diffraction setup, on the beam emerging from fluorophore 80 iszero. Therefore, the conical crystal does not change the geometry of thefluorescent light emitted by the fluorophore. Light incoming from afluorophore 80′, is a vortex before and after the conical crystal 98.

The fluorophore 80″ had been placed after the focal plane of thecollimating lens, 82, at a distance of Δz on the lens system 98; it isplaced at a distance of −2 Δz of the focal position, 99, and the lightfrom the fluorophore 80″ converge also to the output of the lens system,98, after the front lens, 97. The light from the fluorophore 80″, hasalready been converted into a vortex by one of conical diffraction setupconsisting of collimating lens 81, and either one of the conicalcrystals 88 or 89, depending on the channel of polarization followed bythe light. The conical crystal 101 changes the light from fluorophore80″, and, for relevant parameters of the material, i.e. the size andorientation of the conical crystal, it reverts to a regular wave,slightly different from the Airy disk.

The objective lens of the non-collimation path, 102, is adapted to focusthe plane containing fluorophore 80″, which is a regular wave, 104, andnot the fluorophore 80′, which is singular on the pixelated detectorassembly, 103. The incident light emerging from a fluorophore positionedin plane 104, such as the fluorophore 80″, is perfectly focused and ispositioned at the center of the pixelated detector, 103. Incident lightemerging from a fluorophore positioned at the plane 99 is a vortex andtherefore focuses on an outer ring with a central zero. By separatelyrecording the intensity at the center and the intensity at the outerpart of the detector, it is possible to separate, with a slight overlapbetween the incident light planes 104 and 99. In addition, a fluorophorepositioned at the plane 104 as the fluorophore 80, is slightlydelocalized because the objective is calculated so as to focus on thedetector plane 104. This improves the action of the optical moduleLongSRCS, pushing further the intensity of the vortex center andreducing duplication.

This simplified description of a preferred embodiment of the opticalmodule LongSRCS, 800, allows many possibilities of variations andadaptations by changes in the optical design through changes known toone skilled in the art. These changes include, but are not limited to:the crystal material and orientations, the choice of polarizationcomponents, the choice of the polarization axes of the cascade elements,the number of sensors, or, reversing the roles of fluorophores 80′ and80″. In addition, the module is ideally conditioned to be constructed asa set of monolithic subsets or even as a single monolithic unit.

Method PDOS and Lateral Measurements

Method PDOS was originally designed to allow longitudinalsuperresolution, however PDOS method can also be used for measuring thelateral position of a fluorophore. Indeed, the elementary lightdistributions are also sensitive to variation of the lateral position ofthe fluorophore. For a plane sample, in the case where the lightprojection is not possible, the method PDOS may replace the method PSITfor performing superresolution measurements

All these variants of the measurement methodology are considered part ofthe invention. The inventor has yet chosen in the preferredimplementation to separate into two disjoint, separated, butcomplementary optical modules the lateral measures from the longitudinalmeasures to reduce the complexity of each one of the add-ons.

Detection Module

The corollary of the potency of the measurement methodology is therequirement of a more complex detection module, able to detect andretrieve information created. In scanning confocal microscopy, thedetector is a detector consisting of a single element as a PMT or SPAD.The acquisition time of the detector is determined by the scanningmechanism.

The measurement methodology requires, in some embodiments, two detectormodules, instead of one, the fundamental and vortex detector modules. Inaddition, the measurement methodology requires, in some embodiments, foreach illuminated volume, the acquisition of the optical information on asmall spatial grid, typically 16*16, at a rate higher than the pixeltime, due to the requirement to identify and quantify the sequentialsignals.

An improved detection module, 65, may be implemented using smalldetectors with low number of pixels. Such a module would not have beenpossible ten or twenty years ago, due to the lack of appropriatetechnologies. Today, small detectors with small number of pixels, athigh speed, with low noise characteristics are available on the basis ofseveral technologies: SPAD arrays with a small number of pixels, such as32*32 have been shown recently with acquisition rates up to 1 MHz. Theimproved detector module 65, may also be implemented using CCD, EMCCD orCMOS sensors. CCD sensors, CMOS and EMCCD with a small number of pixelsexist or can be specifically designed. In addition, CCD sensors, CMOSEMCCD can be used using features as region of interest, sub-windowing or“binning”, available in many detectors.

The spatio-temporal information referenced herein is the position andthe time of the impact of each fluorescent photon. In real systems, thespatio-temporal information is corrupted by the noise of the detector,which creates incorrect photons, and by inefficient detection, creatingphotons which are not detected, thereby reducing performance. In SPADarrays, for each photon, the pixel that has detected it and the time ofimpact are received, i.e. the full spatiotemporal information isavailable. For CCD sensors, CMOS or EMCCD, the acquisition of multipleframes is necessary to approximate the spatio-temporal information.

In several implementations we will refer to separate detectors; in manycases the sensor can be either physically separated or consisting ofdifferent areas on a single detector, or a combination of the twoprevious cases.

Algorithms SRCDA

As stated previously, the algorithmic SRCDA can be implemented using theinverse problem methods of estimating parameters methods known to thoseskilled in the art.

We also present an algorithm according to one embodiment, specific tothe measurement methodology, based on a set of descriptors.

Referring now to FIG. 9 , which is a simplified schematic illustrationof a algorithmic method, 900, of superresolution of fluorophore's datain accordance with an embodiment of the present invention.

An algorithmic procedure, presented in the FIG. 9 , quantifies thenumber of fluorophores, retrieves the attributes of each fluorophore andquantifies the accuracy of each output parameter.

The preprocessing procedure, 111, reorganized the spatiotemporalinformation, 110, in sets of superresolution images, 112. This can bedone using a filter bank procedure. The data set is then a small seriesof small images, typically 16*16 pixels. The pretreatment procedure isapplied to a small number, of the order of several thousand, ofspatiotemporal elements; it can be performed in real time using existinghardware.

The procedure descriptor, 113, the main step of the calculation, createdfrom each image, a set of descriptors, 114, and their statisticalsignificance. Descriptors include, but are not limited to: the intensityof each image, the presence in the image of a light distribution and itscharacterization as a regular distribution or as a vortex, the center ofgravity, and moments of first and higher orders.

The third step is a filtering operation, 115, wherein only thedescriptors that are statistically relevant, are retained.

The classification operation, 116, is the last step of the algorithm.The algorithm is capable of recognizing, on the basis of the set ofdescriptors, 114, and a knowledge base, 117, where the measurementdifferent cases as a single fluorophore, two fluorophores separatedlongitudinally or laterally and three or more fluorophores.

Note that, due to the amount of information created, numerous cases thatwere ambiguous in fluorescence microscopy will be clearly identified.For example, as described in more detail later, a single fluorophoremust meet a long list of conditions and cannot be confused with a caseof multi-fluorophore. Two longitudinally separated fluorophores willcreate independent sets of descriptors and two laterally separatedfluorophores differ clearly on at least one descriptor from a singlefluorophore.

Algorithm Process Consists Implementing Optical Measurement Methodology

The compound optical process according to at least one embodiment of theinvention is the logical complement of the descriptors algorithm.Indeed, the result of the descriptors calculation procedure can lead tothe conclusion that an additional image would improve performance of themeasurement. The SRCDP microscopy platform allows the acquisition ofone—or more additional images from a set of light distribution of thePSIT or PDOS methods.

An example is explained below.

Position Measuring Point by the Method PSIT

PSIT method can be used as a technique for measuring the position of afluorophore with high precision. This measure can use the descriptorsalgorithm presented previously.

Consider a fluorophore positioned at the position x, y in Cartesiancoordinates and (ρ, θ) in polar coordinates.

A sequence of illumination consisting of a fundamental wave, and acouple of the so-called “half-moon” distributions aligned alongorthogonal axes is projected onto the fluorophore.

The preprocessing procedure created two images:

-   -   A “top hat” image consisting of the sum of the three images of        the sequence.    -   A vortex image consisting of the sum of the two images        half-moons.    -   A first descriptor is the Cartesian position is calculated using        the algorithm of the centroid of the image “top hat”.

Referring to FIG. 10 , the radial position p can be measuredunambiguously by measuring a parameter, ρ_(a), equal to the arctangent,of the intensity ratio between the normalized intensity emitted byilluminated by the fluorophore wave vortex, I_(v), and the normalizedintensity emitted by the fluorophore illuminated by the fundamentalwave, I_(F), normalized by a factor π. In fact:

-   -   The normalized intensity emitted by the fluorophore illuminated        by the fundamental wave varies from 1, at the center of the        fundamental wave, to 0, at radius of Airy,    -   the normalized intensity, emitted by the fluorophore illuminated        by the vortex wave varies from 0 for the center of the vortex to        1 at the vortex maximum and reach 0 to a value slightly higher        than the radius of Airy. The arc tangent of the ratio is a        monotonic function.

The azimuth position can be measured by measuring the intensity ratiobetween the total intensity emitted by the fluorophore illuminated bythe first half-moon distribution, I_(H), and the total intensity emittedby the fluorophore illuminated by the second half moon distribution,I_(ve). The ratio between these two intensities is a geometric tangentsquare law:

$\begin{matrix}{\frac{I_{VE}}{I_{H}} = {\tan^{2}\theta}} & \left( {{EQ}.9} \right)\end{matrix}$

Both measures are redundant. This redundancy is a measure to qualify theobserved object as a single point and separate it from other objectspotentially present in the sample.

Representation in a Higher Dimensional Space: CartesianoPolarRepresentation

This result can be generalized. We introduce in this paper an entire newrepresentation of a plane, combining the Cartesian representation andthe polar representation. We named this representation theCartesianoPolar representation. A point in the plane is represented by aquadruplet: x, y, p, θ. This representation is non-Euclidean andredundant. A similar representation of space can be defined mutatismutandis.

At first sight this representation seems unnecessary: it is a highlycomplex representation for a much simpler reality. It is well known thatthe position of a point in a plane can be represented, alternatively,either by using the Cartesian coordinates, x and y, or either by usingpolar coordinates p and θ.

Representation in a Higher Dimensional Space: Pythagoras Space

In this paper only the simplified version of the CartesianoPolarrepresentation is detailed, wherein a point with coordinates x, y and pis represented. We named this space the space of Pythagoras.

Defining the geometric area to be a two-dimensional surface inthree-dimensional space, which fills the constitutive geometric equationρ²=x²+y²; assumes a measurement system that simultaneously measures x, yand ρ, as the measurement system such as described in the previousparagraph together with a centroid algorithm on the same data. A pointwill be physically positioned in the space of Pythagoras, on thegeometrical surface. Consider the case of two or more physical points:The center of gravity of the two points of measurement is outside thegeometric surface and creates a point outside this area. Thisrepresentation is a mathematical formalization and generalization of thedeterministic algorithm for separating the case of an isolated pointfrom that of an aggregate of points previously described.

Recognition and Measurement of Two Points: A New Resolution Criterion

Consider now two fluorophores positioned symmetrically about the centerat positions, ρ, θ and ρ, −θ in polar coordinates. We will use thesystem described in the previous paragraphs. Three descriptors give thefollowing results:

The centroid measure the centroid of the light distribution, which willbe the origin,

-   -   The identifier ρ, measure the value of the common radial value        of the two fluorophores,    -   The θ descriptor, which in the case of half-moons contains a        degeneracy between θ and −θ, will measure the value θ.

As mentioned above, if the value of the descriptor p is not zero, weknow that the case study is not a point but two or more. In addition,descriptors p and 0 allow us to measure the characteristics of the twopoints at a much higher resolution than that defined by the Rayleighcriterion. Moreover, using a compound process it is possible to separatethis case from the vast majority of cases of three or more points. Anadditional light distribution can be projected onto the sample, ahalf-moon inclined at an angle θ; the assumption of the presence of twopoints will be confirmed or refuted based on the results of this image.Indeed, the measured energy will be zero for two points, for a line orfor a series of dots aligned in the direction of the angle θ.

Control Module

With reference to FIG. 11 , the preferred embodiment of this invention,the invention further describes the various control elements integratedinto the platform SRCDP, 500:

The control module, 1100 (shown in FIG. 5 ), using the procedure ofsystemic control, 1101, monitors and modifies the optical parameters ofthe platform SRCDP, 500, the electronic parameters of the improveddetection module, 65, and the mathematical parameters of algorithmicprocedures SRCDA, 600, to optimize the emerging information inaccordance with criteria defined by the system or by the user. Controlis achieved by varying control systems 1102, 1103 and 1104, of thevarious elements of the platform, 600, 800 and 900. The control system1100, also use, if available, external information, 1105, relayed bycomputer support.

Alternative Implementations of the Measurement Methodology

In one embodiment of the PSIT method, regular and singular waves arecreated by the propagation of a incident regular wave through a uniaxialcrystal, replacing the conical crystal 32.

In another embodiment of the method PSIT, regular and singular waves arecreated by the positioning at the Fourier plane of an optical system ofa phase plate—such as a spiral phase plate—or a subwavelength grating,or by positioning a suitable holographic optical element.

In another embodiment of the PSIT method—thick point, not shown, theillumination of the sample comprises a sequence of at least two compactcompound light distributions, every compact compound light distributionbeing composed consisting itself of at least two simple compact lightdistributions projected simultaneously. Said at least two simple compactlight distribution being optically coherent, partially coherent orincoherent relative to each other, said at least two simple compactlight distributions being positioned at different spatial positions andsaid at least two simple compact light distributions differing in atleast one of characteristics, such as their central lateral position,their central longitudinal position, their polarization, amplitude orphase. The ensemble of simple compact light distributions containscompact light distributions from different topological families.

In another embodiment of the PSIT method, not shown, compact lightdistributions are created by different modes of a multimode laser, andthe sequence of compact light distributions is created by successivelycreating modes or, alternatively, by controlling the balance of energybetween the modes.

In another embodiment of the PSIT method, not shown, the relationshipbetween regular and singular wave is dynamically changed.

In another embodiment of the PSIT method, not shown, the regular waveand the singular wave are created by a physical separation of theincident beam—in at least—two paths, the transformation in one path, ofthe regular beam to singular being realized by known means such as phaseplates or spiral phase plates, holographic optical element,subwavelength gratings, uniaxial or biaxial crystals or combinationthereof, and the recombination of the two beams using a beam combinerinto a single beam. In this embodiment, the differentiation of thecompact light distributions can be performed either on the combined beamor on each beam, independently after separation and beforerecombination.

In another embodiment of the method PSIT, dynamic following, not shown,the system comprises means, including but not limited to controllablemirrors, electro-optical or acousto-optical devices or piezoelectricactuators capable to move the compact light distribution or the sequenceof compact light distributions in space with high precision. In thesystem of dynamic monitoring, the position of the compact lightdistribution and of the sequence is dynamically controlled so as tofollow at least one specific target.

In another embodiment of the method PSIT, black fluorophore, not shown,the compact light distribution or a mathematical combination of compactlight distributions is configured so that there is zero intensity at thecenter of the compact light distribution. The system comprises meansadapted to move through space the compact light distribution and thesemeans are used to follow the fluorophore and for positioning thefluorophore at its center, a function of time. When the fluorophore ispositioned at the center of the compact light distribution, withoutmovement, its position can be measured with high accuracy withoutfluorescent light emerging from a fluorophore, thereby substantiallyreducing the effects of photo-bleaching. A movement of the fluorophorecan be compensated by appropriate movement of the position of thecompact light distribution to follow the fluorophore using a smallamount of emitted fluorescent light.

In another embodiment of the method PSIT, dynamic sequences choice, notshown, the system dynamically determines, on the basis of a positioninghypothesis or of a first set of measures, the optimal sequence ofcompact light distributions.

In another embodiment of the method PSIT, sequences choice and dynamicpositioning of the compact light distribution, not shown, the systemcomprises means, including but not limited to controllable mirrors,electro-optic and acousto-optic devices or piezoelectric actuators,capable of moving in space the compact light distribution, or acombination of compact light distributions with great precision. Thesystem dynamically determines, on the basis of a positioning hypothesisor of a first set of measures, the optimal sequence and the position ofthe compact light distributions.

In another embodiment of the PSIT method, PSIT method of triangulation,two or more measurement process of the method PSIT, previouslydescribed, are carried out on the same sample with different projectionaxes. The variation in lateral position between the two measurementspermits the measurement of the longitudinal position of nanoemitterlight.

In another embodiment of the PSIT method, the parallel PSIT method,light is incident on a micro lens array—or other optical means, known tothose skilled in the art, allowing the realization of a set of lightdistributions in parallel, these light distributions being modified byan optical module to perform simultaneously the PSIT method on a largenumber of discrete points.

In another embodiment of the PSIT method the multispectral PSIT method(not shown), the sample is illuminated sequentially or simultaneously byat least two illumination sequences, each sequence projecting light ontothe sample at different wavelengths

In another embodiment of the method PDOS, not shown, the channeling ofthe incoming light from different point sources according to theirlongitudinal position is realized in the focal plane. It is carried outusing an element having polarization properties dependent on the lateralposition. Light entering from a point disposed longitudinally relativeto a determined plane, will be incident on a given position and willhave specific polarization properties, and the incident light frompoints located at different longitudinal—and lateral—positions, will beincident on other positions in the focal plane, which have differentpolarization characteristics.

As to a further discussion of the manner of usage and operation of theinvention, it should be apparent from the above description. Therefore,any discussion on the form of the use and operation will not bedescribed.

In this respect, before explaining at least one embodiment of theinvention in detail, it is understood that the invention is not limitedin its application to the details of construction and arrangements ofthe components set forth in the following description or illustrated inthe drawing. The invention is capable of other embodiments and can bepracticed and carried out in various ways. In addition, it is understoodthat the phraseology and terminology employed herein are for the purposeof description and should not be regarded as limiting.

References cited herein teach many principles that are applicable to thepresent invention. Therefore, the entire contents of these publicationsare incorporated herein by reference, as appropriate to the teachings ofadditional or alternative details, features and/or technicalinformation.

The embodiments of the invention described can be integrated on afluorescence confocal microscope. Superresolution system according toembodiments of the invention is a new method of measurement, in additionto or in replacement of existing methods of microscopy. However, thesuperresolution system according to embodiments of the invention mayequally be integrated on other microscopy platforms. These microscopyplatforms, as described as examples, include but are not limited to:wide field microscopes, Bright field microscope, dark field microscopes,polarization microscopes, phase difference microscopes, differentialinterference contrast microscopes, stereo microscopes, Ramanmicroscopes, microscopes dedicated to a specific task, such as live cellimaging, cell sorting, cell motility or any other instrument opticalmicroscopy as described for example in Nikon (2011).

It is understood that the invention is not limited in its application tothe details set forth in the description contained herein or illustratedin the drawings.

The invention is capable of other embodiments and of being practiced andcarried out in various ways. Those skilled in the art will readilyunderstand that various modifications and changes can be applied to theembodiments of the invention as described above without departing fromits scope as defined in and by the appended claims.

What is claimed is:
 1. A method of optical measurement for determiningthe spatial position of at least one luminous object in a sample, themethod comprising: projecting onto the sample a sequence of a firstcompact luminous distribution and a second compact luminousdistribution, wherein the first and second compact luminousdistributions are of different topological families; formatting, in amanner selected from the group consisting of static and dynamic, theprojected sequence of the first and second compact luminousdistributions to provide a polarization state configured to mitigatevector effects; detecting light re-emitted by said at least one luminousobject of the sample; generating from the detected light a first imageof the at least one luminous object as illuminated by the first compactluminous distribution and a second image of the at least one luminousobject as illuminated by the second compact luminous distribution; andalgorithmically analyzing images to obtain spatial position informationof said at least one luminous object.
 2. A method according to claim 1,wherein formatting the projected sequence includes formatting theprojected sequence to provide the polarization state in a form that isstatic and rotationally symmetrical.
 3. A method according to claim 2,wherein formatting the projected sequence includes formatting theprojected sequence to provide the polarization state in a form that iscircular.
 4. A method according to claim 1, wherein formatting theprojected sequence includes formatting the projected sequence to providethe polarization state in a form that is radial.
 5. A method accordingto claim 1, wherein formatting the projected sequence includesformatting the projected sequence to provide the polarization state in aform that is azimuthal.
 6. A method according to claim 1, whereinformatting the projected sequence includes formatting the projectedsequence to provide the polarization state in a form that is dynamic.